diff --git a/include/boost/multi/detail/index_range.hpp b/include/boost/multi/detail/index_range.hpp
index efc52c0f0..21c0682a5 100644
--- a/include/boost/multi/detail/index_range.hpp
+++ b/include/boost/multi/detail/index_range.hpp
@@ -178,7 +178,7 @@ class range {
 			++curr_;
 			return *this;
 		}
-		constexpr auto operator--() -> const_iterator& {
+		constexpr auto operator--() noexcept(noexcept(--curr_)) -> const_iterator& {
 			--curr_;
 			return *this;
 		}
@@ -344,8 +344,17 @@ struct extension_t : public range<IndexType, IndexTypeLast> {
 	BOOST_MULTI_HD constexpr extension_t(IndexTypeLast last) noexcept  // NOLINT(google-explicit-constructor,hicpp-explicit-conversions) // NOSONAR(cpp:S1709) allow terse syntax
 	: range<IndexType, IndexTypeLast>(IndexType{}, IndexType{} + last) {}
 
+	extension_t(extension_t const&) = default;
+	extension_t(extension_t&&)      = default;
+
+	auto operator=(extension_t const&) -> extension_t& = default;
+	auto operator=(extension_t&&) -> extension_t&      = default;
+
+	~extension_t() = default;
+
 	template<
 		class OtherExtension,
+		std::enable_if_t<!std::is_base_of_v<extension_t, OtherExtension>, int> =0,  // NOLINT(modernize-use-constraints,modernize-type-traits)
 		decltype(
 			detail::implicit_cast<IndexType>(std::declval<OtherExtension>().first()),
 			detail::implicit_cast<IndexTypeLast>(std::declval<OtherExtension>().last())
@@ -365,7 +374,9 @@ struct extension_t : public range<IndexType, IndexTypeLast> {
 	// BOOST_MULTI_HD constexpr explicit extension_t(OtherExtension const& other) noexcept
 	// : extension_t{other.first(), other.last()} {}
 
-	template<class OtherExtension>
+	template<class OtherExtension,
+		std::enable_if_t<!std::is_base_of_v<extension_t, OtherExtension>, int> =0  // NOLINT(modernize-use-constraints,modernize-type-traits)
+	>
 	BOOST_MULTI_HD constexpr auto operator=(OtherExtension const& other) -> extension_t& {
 		(*this) = extension_t{other};
 		return *this;
diff --git a/include/boost/multi/detail/layout.hpp b/include/boost/multi/detail/layout.hpp
index 121a888f5..686571fe9 100644
--- a/include/boost/multi/detail/layout.hpp
+++ b/include/boost/multi/detail/layout.hpp
@@ -123,7 +123,7 @@ class f_extensions_t {
 		}
 	}
 
-	class iterator {
+	class iterator : public weakly_incrementable_facade<iterator>, weakly_decrementable_facade<iterator> {  // NOLINT(fuchsia-multiple-inheritance)
 		typename extensions_t<D>::iterator it_;
 		Proj proj_;
 
@@ -132,14 +132,21 @@ class f_extensions_t {
 		friend f_extensions_t;
 
 	 public:
+		iterator() = default;
+		
 		using iterator_category = std::random_access_iterator_tag;
 
-		auto operator++() -> auto& { ++it_; return *this; }
-		auto operator--() -> auto& { --it_; return *this; }
+		constexpr auto operator++() -> auto& { ++it_; return *this; }
+		constexpr auto operator--() -> auto& { --it_; return *this; }
 
 		constexpr auto operator+=(difference_type dd) -> auto& { it_+=dd; return *this; }
 		constexpr auto operator-=(difference_type dd) -> auto& { it_-=dd; return *this; }
 
+		constexpr auto operator+(difference_type dd) const { return iterator{*this} += dd; }
+		constexpr auto operator-(difference_type dd) const { return iterator{*this} -= dd; }
+
+		friend constexpr auto operator+(difference_type dd, iterator const& self) { return self + dd; }
+
 		friend constexpr auto operator-(iterator const& self, iterator const& other) { return self.it_ - other.it_; }
 
 		friend constexpr auto operator==(iterator const& self, iterator const& other) -> bool { return self.it_ == other.it_; }
@@ -147,10 +154,12 @@ class f_extensions_t {
 
 		friend auto operator<=(iterator const& self, iterator const& other) -> bool { return self.it_ <= other.it_; }
 		friend auto operator< (iterator const& self, iterator const& other) -> bool { return self.it_ <  other.it_; }
+		friend auto operator> (iterator const& self, iterator const& other) -> bool { return self.it_ >  other.it_; }
+		friend auto operator>=(iterator const& self, iterator const& other) -> bool { return self.it_ >= other.it_; }
 
 		constexpr auto operator*() const -> decltype(auto) {
 			using std::get;
-			if constexpr(D != 1) {
+			if constexpr(D > 1) {
 				auto ll = [idx = get<0>(*it_), proj = proj_](auto... rest) { return proj(idx, rest...); };
 				return f_extensions_t<D - 1, decltype(ll)>(extensions_t<D - 1>(get<1>(*it_).base().tail()), ll);
 			} else {
@@ -158,6 +167,8 @@ class f_extensions_t {
 			}
 		}
 
+		using value_type = int;  // decltype(*std::declval<iterator&>());
+
 		auto operator[](difference_type dd) const { return *((*this) + dd); }  // TODO(correaa) use ra_iterator_facade
 	};
 
@@ -239,7 +250,7 @@ struct extensions_t : boost::multi::detail::tuple_prepend_t<index_extension, typ
 
 	using element = boost::multi::detail::tuple_prepend_t<index_extension::value_type, typename extensions_t<D - 1>::element>;
 
-	extensions_t()    = default;
+	constexpr extensions_t()    = default;
 
 	template<class T = void, std::enable_if_t<sizeof(T*) && D == 1, int> = 0>  // NOLINT(modernize-use-constraints) TODO(correaa)
 	// cppcheck-suppress noExplicitConstructor ; to allow passing tuple<int, int> // NOLINTNEXTLINE(runtime/explicit)
@@ -387,12 +398,12 @@ struct extensions_t : boost::multi::detail::tuple_prepend_t<index_extension, typ
 	template<class... Indices>
 	BOOST_MULTI_HD constexpr auto operator()(index idx, Indices... rest) const { return to_linear(idx, rest...); }
 
-	class iterator {
+	class iterator : weakly_incrementable_facade<iterator>, weakly_decrementable_facade<iterator> {  // NOLINT(fuchsia-multiple-inheritance,cppcoreguidelines-pro-type-member-init,hicpp-member-init)
 		index idx_;
 		extensions_t<D - 1> rest_;
 		friend extensions_t;
 	
-		iterator(index idx, extensions_t<D - 1> rest) : idx_{idx}, rest_{rest} {}
+		constexpr iterator(index idx, extensions_t<D - 1> rest) : idx_{idx}, rest_{rest} {}
 
 	 public:
 		using difference_type = index;
@@ -401,6 +412,11 @@ struct extensions_t : boost::multi::detail::tuple_prepend_t<index_extension, typ
 		using reference = value_type;
 		using iterator_category = std::random_access_iterator_tag;
 
+		iterator() = default;
+
+		constexpr auto operator+=(difference_type d) -> iterator& { idx_ += d; return *this; }
+		constexpr auto operator-=(difference_type d) -> iterator& { idx_ -= d; return *this; }
+
 		constexpr auto operator+(difference_type d) const { return iterator{idx_ + d, rest_}; }
 		constexpr auto operator-(difference_type d) const { return iterator{idx_ - d, rest_}; }
 
@@ -683,6 +699,10 @@ template<> struct extensions_t<0> : tuple<> {
 	: base_{tup} {}
 
 	extensions_t() = default;
+	// template<class T1>
+	// cppcheck-suppress noExplicitConstructor ; to allow passing tuple<int, int>  // NOLINTNEXTLINE(runtime/explicit)
+	// BOOST_MULTI_HD explicit constexpr extensions_t(tuple<> /*extensions*/)  // NOLINT(google-explicit-constructor,hicpp-explicit-conversions)
+	// : base_{} {}
 
 	BOOST_MULTI_HD constexpr auto base() const& -> base_ const& { return *this; }
 	BOOST_MULTI_HD constexpr auto base() & -> base_& { return *this; }
@@ -811,6 +831,45 @@ template<> struct extensions_t<1> : tuple<multi::index_extension> {
 		return elements_t{get<0>(static_cast<tuple<multi::index_extension> const&>(*this))};
 	}
 
+	class iterator : weakly_incrementable_facade<iterator>, weakly_decrementable_facade<iterator> {  // NOLINT(fuchsia-multiple-inheritance)
+		index idx_;
+		extensions_t<0> rest_;
+		friend extensions_t;
+	
+		constexpr iterator(index idx, extensions_t<0> rest) : idx_{idx}, rest_{rest} {}
+
+	 public:
+		using difference_type = index;
+		using value_type = decltype(ht_tuple(std::declval<index>(), std::declval<extensions_t<0>>().base()));
+		using pointer = void;
+		using reference = value_type;
+		using iterator_category = std::random_access_iterator_tag;
+
+		iterator() = default;
+
+		constexpr auto operator+=(difference_type d) { idx_+=d; return *this; }
+		constexpr auto operator-=(difference_type d) { idx_-=d; return *this; }
+
+		constexpr auto operator+(difference_type d) const { return iterator{idx_ + d, rest_}; }
+		constexpr auto operator-(difference_type d) const { return iterator{idx_ - d, rest_}; }
+
+		friend constexpr auto operator-(iterator const& self, iterator const& other) -> difference_type { return self.idx_ - other.idx_; }
+
+		constexpr auto operator++() -> auto& { ++idx_; return *this; }
+		constexpr auto operator--() -> auto& { --idx_; return *this; }
+
+		constexpr auto operator*() const {
+			// multi::detail::what(rest_);
+			return ht_tuple(idx_, rest_.base());
+		}
+
+		friend constexpr auto operator==(iterator const& self, iterator const& other) { assert( self.rest_ == other.rest_ ); return self.idx_ == other.idx_; }
+		friend constexpr auto operator!=(iterator const& self, iterator const& other) { assert( self.rest_ == other.rest_ ); return self.idx_ != other.idx_; }
+	};
+
+	constexpr auto begin() const noexcept { return iterator{this->base().head().first(), extensions_t<0>(this->base().tail())}; }
+	constexpr auto end()   const noexcept { return iterator{this->base().head().last() , extensions_t<0>(this->base().tail())}; }
+
 	constexpr auto size() const {
 		using std::get;
 		return get<0>(static_cast<tuple<multi::index_extension> const&>(*this)).size();
diff --git a/include/boost/multi/detail/operators.hpp b/include/boost/multi/detail/operators.hpp
index f66fe2ee3..00e18ed88 100644
--- a/include/boost/multi/detail/operators.hpp
+++ b/include/boost/multi/detail/operators.hpp
@@ -121,6 +121,22 @@ struct weakly_incrementable {
 	// friend T& operator++(weakly_incrementable& t){return ++static_cast<T&>(t);}
 };
 
+template<class Self> class default_initializable_facade {
+	default_initializable_facade() = default;
+};
+
+template<class Self> class weakly_incrementable_facade : selfable<Self> {
+	weakly_incrementable_facade() = default;
+	friend Self;
+	friend constexpr auto operator++(Self& self, int) -> Self { Self ret = self; ++self; return ret; }
+};
+
+template<class Self> class weakly_decrementable_facade : selfable<Self> {
+	weakly_decrementable_facade() = default;
+	friend Self;
+	friend constexpr auto operator--(Self& self, int) -> Self { Self ret = self; --self; return ret; }
+};
+
 template<class T>
 struct weakly_decrementable {
  protected:
diff --git a/test/extensions.cpp b/test/extensions.cpp
index 94c9c5973..83adf07cd 100644
--- a/test/extensions.cpp
+++ b/test/extensions.cpp
@@ -7,13 +7,16 @@
 
 #include <boost/core/lightweight_test.hpp>  // IWYU pragma: keep
 
-#include <algorithm>    // IWYU pragma: keep  // for std::equal
+#include <algorithm>  // IWYU pragma: keep  // for std::equal
+#include <iostream>
 #include <tuple>        // IWYU pragma: keep
 #include <type_traits>  // for std::is_same_v
 // IWYU pragma: no_include <variant>        // for get, iwyu bug
 
 #if defined(__cplusplus) && (__cplusplus >= 202002L)
-#include <ranges>  // IWYU pragma: keep  // NOLINT(misc-include-cleaner)
+#include <concepts>  // for default_initializable
+#include <iterator>  // for reverse_iterator, input...
+#include <ranges>    // IWYU pragma: keep  // NOLINT(misc-include-cleaner)
 #endif
 
 namespace multi = boost::multi;
@@ -448,18 +451,117 @@ auto main() -> int {  // NOLINT(bugprone-exception-escape,readability-function-c
 		}
 #endif
 	}
+	{
+		auto xs2D = multi::extensions_t(10, 20);
+		BOOST_TEST( xs2D.size() == 10 );
+		BOOST_TEST( xs2D.num_elements() == 200 );
+
+		using std::get;
+		BOOST_TEST( get<0>(xs2D[3][5]) == 3 );
+		BOOST_TEST( get<0>(xs2D[4][5]) == 4 );
+
+		BOOST_TEST( get<0>((* xs2D.begin() )[5]) == 0 );
+		BOOST_TEST( get<0>((*(xs2D.end()-1))[5]) == 9 );
+
+#if !defined(__NVCC__) && !defined(__NVCOMPILER)  // this CTAD gives a compile error in nvhpc 22.7 and nvcc 12.0
+		multi::extensions_t const xs2D_copy(xs2D);
+#else
+		multi::extensions_t<1> const xs2D_copy(xs2D);
+#endif
+		BOOST_TEST( xs2D_copy == xs2D );
+
+		boost::multi::extensions_t<2>::iterator beg = xs2D.begin();
+		beg++;
+
+		static_assert(std::is_constructible_v<boost::multi::extensions_t<1>::iterator, boost::multi::extensions_t<1>::iterator>);
+
+#if defined(__cpp_lib_ranges) && (__cpp_lib_ranges >= 201911L) && !defined(_MSC_VER)
 
+		static_assert(std::weakly_incrementable<boost::multi::extensions_t<2>::iterator>);
+
+		BOOST_TEST( get<0>(*std::ranges::begin(xs2D)) == 0 );
+		BOOST_TEST( get<0>(*(std::ranges::end(xs2D)-1)) == 9 );
+
+		static_assert(std::ranges::range<std::remove_cvref_t<boost::multi::extensions_t<2>&>>);
+
+		BOOST_TEST( get<0>((*(xs2D.end()-1))[5]) == 9 );
+
+		static_assert(std::ranges::bidirectional_range<multi::extensions_t<2>>);
+
+		auto rxs2D = xs2D | std::views::reverse;
+
+		BOOST_TEST( get<0>((*std::ranges::begin(rxs2D))[5]) == 9 );
+		BOOST_TEST( get<0>((*(std::ranges::end(rxs2D)-1))[5]) == 0 );
+#endif
+	}
 	{
 		auto xs1D = multi::extensions_t(10);
 		BOOST_TEST( xs1D.size() == 10 );
 		using std::get;
 		BOOST_TEST( get<0>(xs1D[3]) == 3 );
+		BOOST_TEST( get<0>(xs1D[4]) == 4 );
+
+		std::cout << "line 500: lhs " << get<0>(*xs1D.begin()) << '\n';
+		BOOST_TEST( get<0>(*xs1D.begin()) == 0 );
 
-		auto v1D = [](auto ii) { return ii * ii; } ^ multi::extensions_t(10);
+		auto end   = xs1D.end();
+		auto endm1 = end - 1;
+		auto [ii] = *endm1;
+		std::cout << "line 501: lhs " <<ii << '\n';
+		BOOST_TEST( ii == 9 );
+
+		std::cout << "line 503: lhs " << get<0>(*endm1) << '\n';
+		BOOST_TEST( get<0>(*endm1) == 9 );
+
+		multi::extensions_t<1> const xs1D_copy(xs1D);
+		BOOST_TEST( xs1D_copy == xs1D );
+
+		multi::extensions_t<1>::iterator const copy(xs1D.begin());
+		BOOST_TEST( copy == xs1D.begin() );
+
+		static_assert(std::is_constructible_v<boost::multi::extensions_t<1>::iterator, boost::multi::extensions_t<1>::iterator>);
+
+#if defined(__cpp_lib_ranges) && (__cpp_lib_ranges >= 201911L) && !defined(_MSC_VER)
+		BOOST_TEST( get<0>(*std::ranges::begin(xs1D)) == 0 );
+
+		BOOST_TEST( get<0>(*(std::ranges::end(xs1D)-1)) == 9 );
+
+		static_assert(std::ranges::range<std::remove_cvref_t<boost::multi::extensions_t<1>&>>);
+
+		BOOST_TEST( get<0>(*(xs1D.end()-1)) == 9 );
+
+		static_assert(std::ranges::bidirectional_range<multi::extensions_t<1>>);
+
+		auto rxs1D = xs1D | std::views::reverse;
+
+		BOOST_TEST( get<0>(*std::ranges::begin(rxs1D)) == 9 );
+		BOOST_TEST( get<0>(*(std::ranges::end(rxs1D)-1)) == 0 );
+#endif
+
+		auto const v1D = [](auto idx) { return idx * idx; } ^ multi::extensions_t(10);
 		BOOST_TEST( v1D.size() == 10 );
 		BOOST_TEST( v1D.elements().size() == 10 );
+		BOOST_TEST( v1D[0] == 0);
 		BOOST_TEST( v1D[4] == 16 );
+		BOOST_TEST( v1D[9] == 81 );
+		BOOST_TEST( *v1D.begin() == 0 );
+		BOOST_TEST( *(v1D.end() - 1) == 81 );
+
 #if defined(__cpp_lib_ranges) && (__cpp_lib_ranges >= 201911L) && !defined(_MSC_VER)
+#if !defined(__NVCC__) && !defined(__NVCOMPILER)  // produces an error: ‘boost::multi::f_extensions_t<D, Proj>::proj_’ has incomplete type
+		static_assert(std::input_or_output_iterator<decltype(v1D.begin())>);
+		static_assert(std::default_initializable<decltype(v1D.begin())>);
+		static_assert(std::semiregular<decltype(v1D.begin())>);
+#endif
+		BOOST_TEST( std::ranges::begin(v1D) == v1D.begin() );
+		BOOST_TEST( std::ranges::end(v1D) == v1D.end() );
+
+		static_assert(std::ranges::bidirectional_range<decltype(v1D)>);
+		static_assert(std::ranges::random_access_range<decltype(v1D)>);
+		auto rv1D = v1D | std::views::reverse;
+
+		BOOST_TEST( rv1D[0] == 81);
+		BOOST_TEST( rv1D[9] == 0 );
 #endif
 	}
 	return boost::report_errors();
diff --git a/test/index_range.cpp b/test/index_range.cpp
index 7ba4a57bf..063de96eb 100644
--- a/test/index_range.cpp
+++ b/test/index_range.cpp
@@ -13,6 +13,10 @@
 // IWYU pragma: no_include <tuple>                            // for tuple_element<>::type
 #include <type_traits>
 
+#if defined(__cplusplus) && (__cplusplus >= 202002L)
+#include <ranges>  // IWYU pragma: keep  // NOLINT(misc-include-cleaner)
+#endif
+
 namespace multi = boost::multi;
 
 auto main() -> int {  // NOLINT(readability-function-cognitive-complexity,bugprone-exception-escape)
@@ -259,5 +263,27 @@ auto main() -> int {  // NOLINT(readability-function-cognitive-complexity,bugpro
 		BOOST_TEST( sum == 5 + 6 + 7 + 8 + 9 + 10 + 11 );
 	}
 
+	{
+		multi::extension_t<int> const ext(5);
+
+		BOOST_TEST( *ext.begin() == 0 );
+		BOOST_TEST( *(ext.end() - 1) == 4 );
+#if defined(__cpp_lib_ranges) && (__cpp_lib_ranges >= 201911L) && !defined(_MSC_VER)
+
+		BOOST_TEST( *std::ranges::begin(ext) == 0 );
+		BOOST_TEST( *(std::ranges::end(ext)-1) == 4 );
+
+		// static_assert(std::ranges::range<std::remove_cvref_t<boost::multi::extensions_t<1>&>>);
+
+		// BOOST_TEST( get<0>(*(xs1D.end()-1)) == 9 );
+
+		BOOST_TEST( ext[1] == 1 );
+
+		auto rext = ext | std::views::reverse;
+
+		BOOST_TEST( rext[1] == 3 );
+#endif
+	}
+
 	return boost::report_errors();
 }