diff --git a/example/currency.cpp b/example/currency.cpp
index c1527b6e..3d9221fb 100644
--- a/example/currency.cpp
+++ b/example/currency.cpp
@@ -39,8 +39,6 @@ inline constexpr struct great_british_pound : named_unit<"GBP", kind_of<currency
 inline constexpr struct japanese_jen : named_unit<"JPY", kind_of<currency>> {} japanese_jen;
 // clang-format on
 
-static_assert(!std::equality_comparable_with<quantity<euro, int>, quantity<us_dollar, int>>);
-
 #if 0
 
 // if you have only a few currencies to handle
@@ -54,6 +52,11 @@ template<Unit auto From, Unit auto To>
 
 #else
 
+template<AssociatedUnit auto From, AssociatedUnit auto To>
+  requires(get_quantity_spec(From) == currency && get_quantity_spec(To) == currency)
+inline constexpr is_unit_convertible_result mp_units::is_unit_convertible<From, To> =
+  is_unit_convertible_result::non_integral_factor;
+
 [[nodiscard]] std::string_view to_string_view(Unit auto u) { return u.symbol.ascii().c_str(); }
 
 template<Unit auto From, Unit auto To>
@@ -69,23 +72,21 @@ template<Unit auto From, Unit auto To>
 
 #endif
 
-template<ReferenceOf<currency> auto To, ReferenceOf<currency> auto From, typename Rep>
-quantity<To, Rep> exchange_to(quantity<From, Rep> q)
+template<typename Rep, AssociatedUnit From, AssociatedUnit To>
+[[nodiscard]] Rep scale_quantity_number(Rep v, From from, To to)
+  requires(get_quantity_spec(from) == currency && get_quantity_spec(to) == currency)
 {
-  return static_cast<Rep>(exchange_rate<q.unit, get_unit(To)>() * q.number()) * To;
+  return static_cast<Rep>(exchange_rate<from, to>() * v);
 }
 
-template<ReferenceOf<currency> auto To, ReferenceOf<currency> auto From, auto PO, typename Rep>
-quantity_point<To, PO, Rep> exchange_to(quantity_point<From, PO, Rep> q)
-{
-  return static_cast<Rep>(exchange_rate<q.unit, get_unit(To)>() * q.absolute().number()) * To;
-}
+static_assert(!std::equality_comparable_with<quantity<euro>, quantity<us_dollar>>);
 
 int main()
 {
-  auto price_usd = quantity_point{100 * us_dollar};
-  auto price_euro = quantity_point{exchange_to<euro>(price_usd)};
+  auto price_usd = quantity_point{100. * us_dollar};
+  auto price_euro = quantity_point{price_usd[euro]};
 
   std::cout << price_usd.absolute() << " -> " << price_euro.absolute() << "\n";
   // std::cout << price_usd.absolute() + price_euro.absolute() << "\n";  // does not compile
-}
\ No newline at end of file
+  // std::cout << price_euro.absolute() + price_usd.absolute() << "\n";  // does not compile
+}
diff --git a/src/core/include/mp_units/bits/sudo_cast.h b/src/core/include/mp_units/bits/sudo_cast.h
index 1d4b9bf1..9825c815 100644
--- a/src/core/include/mp_units/bits/sudo_cast.h
+++ b/src/core/include/mp_units/bits/sudo_cast.h
@@ -35,6 +35,32 @@ class quantity;
 
 namespace detail {
 
+// The default implementation for the number scaling customization point
+template<typename Rep, Unit From, Unit To>
+[[nodiscard]] constexpr auto scale_quantity_number(Rep v, From from, To to)
+  requires(have_same_canonical_reference_unit(from, to))
+{
+  using multiplier_type = decltype([] {
+    // widen the type to prevent overflows
+    using wider_type = decltype(Rep{} * std::intmax_t{});
+    // check if `wider_type` supports scaling operations
+    if constexpr (requires(wider_type v) { v* v / v; })
+      // if the `wider_type` can handle scaling operations then use it to improve accuracy
+      return wider_type{};
+    else
+      // needed for example for linear algebra where `op/` on matrix types is not available
+      return std::intmax_t{};
+  }());
+
+  constexpr Magnitude auto c_mag = detail::get_canonical_unit(from).mag / detail::get_canonical_unit(to).mag;
+  constexpr Magnitude auto num = numerator(c_mag);
+  constexpr Magnitude auto den = denominator(c_mag);
+  constexpr Magnitude auto irr = c_mag * (den / num);
+
+  constexpr auto val = [](Magnitude auto m) { return get_value<multiplier_type>(m); };
+  return v * val(num) / val(den) * val(irr);
+}
+
 /**
  * @brief Explicit cast of entire quantity
  *
@@ -45,7 +71,7 @@ namespace detail {
 template<Quantity To, auto R, typename Rep>
   requires(castable(get_quantity_spec(R), To::quantity_spec)) &&
           ((get_unit(R) == To::unit && std::constructible_from<typename To::rep, Rep>) ||
-           (get_unit(R) != To::unit))  // && scalable_with_<typename To::rep>))
+           (get_unit(R) != To::unit && convertible(get_unit(R), To::unit)))  // && scalable_with_<typename To::rep>))
 // TODO how to constrain the second part here?
 [[nodiscard]] constexpr Quantity auto sudo_cast(const quantity<R, Rep>& q)
 {
@@ -66,26 +92,11 @@ template<Quantity To, auto R, typename Rep>
       else
         return Rep{};
     }());
-    using multiplier_type = decltype([] {
-      // widen the type to prevent overflows
-      using wider_type = decltype(rep_type{} * std::intmax_t{});
-      // check if `wider_type` supports scaling operations
-      if constexpr (requires(wider_type v) { v* v / v; })
-        // if the `wider_type` can handle scaling operations then use it to improve accuracy
-        return wider_type{};
-      else
-        // needed for example for linear algebra where `op/` on matrix types is not available
-        return std::intmax_t{};
-    }());
 
-    constexpr Magnitude auto c_mag =
-      detail::get_canonical_unit(get_unit(R)).mag / detail::get_canonical_unit(To::unit).mag;
-    constexpr Magnitude auto num = numerator(c_mag);
-    constexpr Magnitude auto den = denominator(c_mag);
-    constexpr Magnitude auto irr = c_mag * (den / num);
-
-    constexpr auto val = [](Magnitude auto m) { return get_value<multiplier_type>(m); };
-    return static_cast<TYPENAME To::rep>(static_cast<rep_type>(q.number()) * val(num) / val(den) * val(irr)) *
+    // `scale_quantity_number` is a customization point
+    // Will be found only via ADL (if provided) for user-defined units
+    return static_cast<TYPENAME To::rep>(
+             scale_quantity_number(static_cast<rep_type>(q.number()), get_unit(R), To::unit)) *
            To::reference;
   }
 }
diff --git a/src/core/include/mp_units/quantity.h b/src/core/include/mp_units/quantity.h
index 4862870e..36bdcbe8 100644
--- a/src/core/include/mp_units/quantity.h
+++ b/src/core/include/mp_units/quantity.h
@@ -50,18 +50,13 @@ template<typename T, typename Arg>
 concept RepSafeConstructibleFrom =  // exposition only
   std::constructible_from<T, Arg> && (treat_as_floating_point<T> || !treat_as_floating_point<Arg>);
 
-// UFrom ratio is an exact multiple of UTo
-template<auto UFrom, auto UTo>
-concept Harmonic =  // exposition only
-  Unit<decltype(UFrom)> && Unit<decltype(UTo)> &&
-  is_integral(get_canonical_unit(UFrom).mag / get_canonical_unit(UTo).mag);
-
 template<typename QFrom, typename QTo>
 concept QuantityConvertibleTo =  // exposition only
   Quantity<QFrom> && Quantity<QTo> && implicitly_convertible(QFrom::quantity_spec, QTo::quantity_spec) &&
   convertible(QFrom::unit, QTo::unit) && requires(QFrom q) { detail::sudo_cast<QTo>(q); } &&
   (treat_as_floating_point<typename QTo::rep> ||
-   (!treat_as_floating_point<typename QFrom::rep> && Harmonic<QFrom::unit, QTo::unit>));
+   (!treat_as_floating_point<typename QFrom::rep> &&
+    is_unit_convertible<QFrom::unit, QTo::unit> == is_unit_convertible_result::integral_factor));
 
 template<quantity_character Ch, typename Func, typename T, typename U>
 concept InvokeResultOf = std::regular_invocable<Func, T, U> && RepresentationOf<std::invoke_result_t<Func, T, U>, Ch>;
diff --git a/src/core/include/mp_units/unit.h b/src/core/include/mp_units/unit.h
index da4d324a..50c4583e 100644
--- a/src/core/include/mp_units/unit.h
+++ b/src/core/include/mp_units/unit.h
@@ -594,11 +594,21 @@ inline constexpr struct percent : named_unit<"%", mag<ratio{1, 100}> * one> {} p
 inline constexpr struct per_mille : named_unit<basic_symbol_text{"‰", "%o"}, mag<ratio(1, 1000)> * one> {} per_mille;
 // clang-format on
 
+// is_unit_convertible customization point
+enum class is_unit_convertible_result { no, integral_factor, non_integral_factor };
 
-// convertible_to
+template<Unit auto From, Unit auto To>
+inline constexpr is_unit_convertible_result is_unit_convertible =
+  detail::have_same_canonical_reference_unit(From, To)
+    ? (is_integral(detail::get_canonical_unit(From).mag / detail::get_canonical_unit(To).mag)
+         ? is_unit_convertible_result::integral_factor
+         : is_unit_convertible_result::non_integral_factor)
+    : is_unit_convertible_result::no;
+
+// convertible
 [[nodiscard]] consteval bool convertible(Unit auto from, Unit auto to)
 {
-  return detail::have_same_canonical_reference_unit(from, to);
+  return is_unit_convertible<from, to> != is_unit_convertible_result::no;
 }
 
 // Common unit