diff --git a/include/boost/multiprecision/detail/number_base.hpp b/include/boost/multiprecision/detail/number_base.hpp
index 2f4db9df..e36f9d66 100644
--- a/include/boost/multiprecision/detail/number_base.hpp
+++ b/include/boost/multiprecision/detail/number_base.hpp
@@ -150,10 +150,17 @@ template <class tag, class Arg1, class Arg2, class Arg3, class Arg4>
 struct is_number_expression<detail::expression<tag, Arg1, Arg2, Arg3, Arg4> > : public std::integral_constant<bool, true>
 {};
 
+namespace detail {
+template <class Val, class Backend>
+struct canonical;
+}
+
 template <class T, class Num>
 struct is_compatible_arithmetic_type
     : public std::integral_constant<bool, 
-          std::is_convertible<T, Num>::value && !std::is_same<T, Num>::value && !is_number_expression<T>::value>
+          std::is_convertible<T, Num>::value && !std::is_same<T, Num>::value && !is_number_expression<T>::value
+          && (std::is_constructible<typename Num::backend_type, typename detail::canonical<T, typename Num::backend_type>::type>::value 
+             || std::is_assignable<typename Num::backend_type, typename detail::canonical<T, typename Num::backend_type>::type>::value || is_number<T>::value || is_number_expression<T>::value)>
 {};
 
 namespace detail {
diff --git a/test/Jamfile.v2 b/test/Jamfile.v2
index 2deef918..3e490a13 100644
--- a/test/Jamfile.v2
+++ b/test/Jamfile.v2
@@ -1240,6 +1240,7 @@ test-suite misc :
                                     [ check-target-builds ../config//has_float128 : <source>quadmath <define>TEST_FLOAT128 ]
                                     <define>TEST_CPP_DEC_FLOAT 
                                     <define>TEST_CPP_BIN_FLOAT ]
+      [ compile git_issue_608.cpp ]
       [ compile git_issue_98.cpp : 
          [ check-target-builds ../config//has_float128 : <define>TEST_FLOAT128 <source>quadmath : ]
          [ check-target-builds ../config//has_gmp : <define>TEST_GMP <source>gmp : ]
diff --git a/test/git_issue_608.cpp b/test/git_issue_608.cpp
new file mode 100644
index 00000000..ee730515
--- /dev/null
+++ b/test/git_issue_608.cpp
@@ -0,0 +1,15 @@
+///////////////////////////////////////////////////////////////////////////////
+//  Copyright 2024 John Maddock. Distributed under the Boost
+//  Software License, Version 1.0. (See accompanying file
+//  LICENSE_1_0.txt or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#include <functional>
+#include <boost/multiprecision/cpp_bin_float.hpp>
+
+using big_float_type = boost::multiprecision::cpp_bin_float_100;
+
+int main()
+{
+   static_assert(boost::multiprecision::is_compatible_arithmetic_type<std::reference_wrapper<big_float_type>, big_float_type>::value == 0, "This should not be a compatible type");
+}
+