diff --git a/src/core/include/mp-units/framework/quantity.h b/src/core/include/mp-units/framework/quantity.h
index bd412072..d2acd5f6 100644
--- a/src/core/include/mp-units/framework/quantity.h
+++ b/src/core/include/mp-units/framework/quantity.h
@@ -463,9 +463,9 @@ public:
   }
 
   // binary operators on quantities
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires detail::CommonlyInvocableQuantities<std::plus<>, quantity, quantity<R2, Rep2>>
-  [[nodiscard]] friend constexpr Quantity auto operator+(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr Quantity auto operator+(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     using ret = detail::common_quantity_for<std::plus<>, quantity, quantity<R2, Rep2>>;
     const ret ret_lhs(lhs);
@@ -474,9 +474,9 @@ public:
                                 ret::reference};
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires detail::CommonlyInvocableQuantities<std::minus<>, quantity, quantity<R2, Rep2>>
-  [[nodiscard]] friend constexpr Quantity auto operator-(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr Quantity auto operator-(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     using ret = detail::common_quantity_for<std::minus<>, quantity, quantity<R2, Rep2>>;
     const ret ret_lhs(lhs);
@@ -485,10 +485,10 @@ public:
                                 ret::reference};
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires(!treat_as_floating_point<Rep>) && (!treat_as_floating_point<Rep2>) &&
             detail::CommonlyInvocableQuantities<std::modulus<>, quantity, quantity<R2, Rep2>>
-  [[nodiscard]] friend constexpr Quantity auto operator%(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr Quantity auto operator%(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     MP_UNITS_EXPECTS_DEBUG(rhs != rhs.zero());
     using ret = detail::common_quantity_for<std::modulus<>, quantity, quantity<R2, Rep2>>;
@@ -498,58 +498,58 @@ public:
                                 ret::reference};
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires detail::InvocableQuantities<std::multiplies<>, quantity, quantity<R2, Rep2>>
-  [[nodiscard]] friend constexpr Quantity auto operator*(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr Quantity auto operator*(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     return ::mp_units::quantity{lhs.numerical_value_ref_in(unit) * rhs.numerical_value_ref_in(rhs.unit), R * R2};
   }
 
-  template<typename Value>
+  template<std::derived_from<quantity> Q, typename Value>
     requires(!Quantity<Value>) &&
             (!Reference<Value>) && detail::InvokeResultOf<quantity_spec.character, std::multiplies<>, Rep, const Value&>
-  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const quantity& q, const Value& v)
+  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Q& q, const Value& v)
   {
     return ::mp_units::quantity{q.numerical_value_ref_in(unit) * v, R};
   }
 
-  template<typename Value>
+  template<typename Value, std::derived_from<quantity> Q>
     requires(!Quantity<Value>) &&
             (!Reference<Value>) && detail::InvokeResultOf<quantity_spec.character, std::multiplies<>, const Value&, Rep>
-  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Value& v, const quantity& q)
+  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator*(const Value& v, const Q& q)
   {
     return ::mp_units::quantity{v * q.numerical_value_ref_in(unit), R};
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires detail::InvocableQuantities<std::divides<>, quantity, quantity<R2, Rep2>>
-  [[nodiscard]] friend constexpr Quantity auto operator/(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr Quantity auto operator/(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     MP_UNITS_EXPECTS_DEBUG(rhs != rhs.zero());
     return ::mp_units::quantity{lhs.numerical_value_ref_in(unit) / rhs.numerical_value_ref_in(rhs.unit), R / R2};
   }
 
-  template<typename Value>
+  template<std::derived_from<quantity> Q, typename Value>
     requires(!Quantity<Value>) &&
             (!Reference<Value>) && detail::InvokeResultOf<quantity_spec.character, std::divides<>, Rep, const Value&>
-  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator/(const quantity& q, const Value& v)
+  [[nodiscard]] friend constexpr QuantityOf<quantity_spec> auto operator/(const Q& q, const Value& v)
   {
     MP_UNITS_EXPECTS_DEBUG(v != quantity_values<Value>::zero());
     return ::mp_units::quantity{q.numerical_value_ref_in(unit) / v, R};
   }
 
-  template<typename Value>
+  template<typename Value, std::derived_from<quantity> Q>
     requires(!Quantity<Value>) &&
             (!Reference<Value>) && detail::InvokeResultOf<quantity_spec.character, std::divides<>, const Value&, Rep>
-  [[nodiscard]] friend constexpr QuantityOf<inverse(quantity_spec)> auto operator/(const Value& v, const quantity& q)
+  [[nodiscard]] friend constexpr QuantityOf<inverse(quantity_spec)> auto operator/(const Value& v, const Q& q)
   {
     return ::mp_units::quantity{v / q.numerical_value_ref_in(unit), ::mp_units::one / R};
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires requires { typename std::common_type_t<quantity, quantity<R2, Rep2>>; } &&
              std::equality_comparable<typename std::common_type_t<quantity, quantity<R2, Rep2>>::rep>
-  [[nodiscard]] friend constexpr bool operator==(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr bool operator==(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     using ct = std::common_type_t<quantity, quantity<R2, Rep2>>;
     const ct ct_lhs(lhs);
@@ -557,10 +557,10 @@ public:
     return ct_lhs.numerical_value_ref_in(ct::unit) == ct_rhs.numerical_value_ref_in(ct::unit);
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity> Q, auto R2, typename Rep2>
     requires requires { typename std::common_type_t<quantity, quantity<R2, Rep2>>; } &&
              std::three_way_comparable<typename std::common_type_t<quantity, quantity<R2, Rep2>>::rep>
-  [[nodiscard]] friend constexpr auto operator<=>(const quantity& lhs, const quantity<R2, Rep2>& rhs)
+  [[nodiscard]] friend constexpr auto operator<=>(const Q& lhs, const quantity<R2, Rep2>& rhs)
   {
     using ct = std::common_type_t<quantity, quantity<R2, Rep2>>;
     const ct ct_lhs(lhs);
diff --git a/src/core/include/mp-units/framework/quantity_point.h b/src/core/include/mp-units/framework/quantity_point.h
index 97d358fc..d9395df3 100644
--- a/src/core/include/mp-units/framework/quantity_point.h
+++ b/src/core/include/mp-units/framework/quantity_point.h
@@ -415,10 +415,10 @@ public:
   }
 
   // binary operators on quantity points
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity_point> QP, auto R2, typename Rep2>
   // TODO simplify when gcc catches up
     requires ReferenceOf<MP_UNITS_REMOVE_CONST(decltype(R2)), PO.quantity_spec>
-  [[nodiscard]] friend constexpr QuantityPoint auto operator+(const quantity_point& qp, const quantity<R2, Rep2>& q)
+  [[nodiscard]] friend constexpr QuantityPoint auto operator+(const QP& qp, const quantity<R2, Rep2>& q)
     requires requires { qp.quantity_ref_from(PO) + q; }
   {
     if constexpr (detail::is_zeroth_point_origin(PO))
@@ -427,19 +427,19 @@ public:
       return ::mp_units::quantity_point{qp.quantity_ref_from(PO) + q, PO};
   }
 
-  template<auto R1, typename Rep1>
+  template<auto R1, typename Rep1, std::derived_from<quantity_point> QP>
   // TODO simplify when gcc catches up
     requires ReferenceOf<MP_UNITS_REMOVE_CONST(decltype(R1)), PO.quantity_spec>
-  [[nodiscard]] friend constexpr QuantityPoint auto operator+(const quantity<R1, Rep1>& q, const quantity_point& qp)
+  [[nodiscard]] friend constexpr QuantityPoint auto operator+(const quantity<R1, Rep1>& q, const QP& qp)
     requires requires { q + qp.quantity_ref_from(PO); }
   {
     return qp + q;
   }
 
-  template<auto R2, typename Rep2>
+  template<std::derived_from<quantity_point> QP, auto R2, typename Rep2>
   // TODO simplify when gcc catches up
     requires ReferenceOf<MP_UNITS_REMOVE_CONST(decltype(R2)), PO.quantity_spec>
-  [[nodiscard]] friend constexpr QuantityPoint auto operator-(const quantity_point& qp, const quantity<R2, Rep2>& q)
+  [[nodiscard]] friend constexpr QuantityPoint auto operator-(const QP& qp, const quantity<R2, Rep2>& q)
     requires requires { qp.quantity_ref_from(PO) - q; }
   {
     if constexpr (detail::is_zeroth_point_origin(PO))
@@ -448,8 +448,8 @@ public:
       return ::mp_units::quantity_point{qp.quantity_ref_from(PO) - q, PO};
   }
 
-  template<QuantityPointOf<absolute_point_origin> QP2>
-  [[nodiscard]] friend constexpr Quantity auto operator-(const quantity_point& lhs, const QP2& rhs)
+  template<std::derived_from<quantity_point> QP, QuantityPointOf<absolute_point_origin> QP2>
+  [[nodiscard]] friend constexpr Quantity auto operator-(const QP& lhs, const QP2& rhs)
     // TODO consider constraining it for both branches
     requires requires { lhs.quantity_ref_from(point_origin) - rhs.quantity_ref_from(QP2::point_origin); }
   {
@@ -460,10 +460,10 @@ public:
              (lhs.point_origin - rhs.point_origin);
   }
 
-  template<PointOrigin PO2>
+  template<std::derived_from<quantity_point> QP, PointOrigin PO2>
     requires QuantityPointOf<quantity_point, PO2{}> &&
              ReferenceOf<std::remove_const_t<decltype(reference)>, PO2::quantity_spec>
-  [[nodiscard]] friend constexpr Quantity auto operator-(const quantity_point& qp, PO2 po)
+  [[nodiscard]] friend constexpr Quantity auto operator-(const QP& qp, PO2 po)
   {
     if constexpr (point_origin == po)
       return qp.quantity_ref_from(point_origin);
@@ -482,17 +482,17 @@ public:
     }
   }
 
-  template<PointOrigin PO1>
+  template<PointOrigin PO1, std::derived_from<quantity_point> QP>
     requires QuantityPointOf<quantity_point, PO1{}> &&
              ReferenceOf<std::remove_const_t<decltype(reference)>, PO1::quantity_spec>
-  [[nodiscard]] friend constexpr Quantity auto operator-(PO1 po, const quantity_point& qp)
+  [[nodiscard]] friend constexpr Quantity auto operator-(PO1 po, const QP& qp)
   {
     return -(qp - po);
   }
 
-  template<QuantityPointOf<absolute_point_origin> QP2>
+  template<std::derived_from<quantity_point> QP, QuantityPointOf<absolute_point_origin> QP2>
     requires std::equality_comparable_with<quantity_type, typename QP2::quantity_type>
-  [[nodiscard]] friend constexpr bool operator==(const quantity_point& lhs, const QP2& rhs)
+  [[nodiscard]] friend constexpr bool operator==(const QP& lhs, const QP2& rhs)
   {
     if constexpr (point_origin == QP2::point_origin)
       return lhs.quantity_ref_from(point_origin) == rhs.quantity_ref_from(QP2::point_origin);
@@ -500,9 +500,9 @@ public:
       return lhs - lhs.absolute_point_origin == rhs - rhs.absolute_point_origin;
   }
 
-  template<QuantityPointOf<absolute_point_origin> QP2>
+  template<std::derived_from<quantity_point> QP, QuantityPointOf<absolute_point_origin> QP2>
     requires std::three_way_comparable_with<quantity_type, typename QP2::quantity_type>
-  [[nodiscard]] friend constexpr auto operator<=>(const quantity_point& lhs, const QP2& rhs)
+  [[nodiscard]] friend constexpr auto operator<=>(const QP& lhs, const QP2& rhs)
   {
     if constexpr (point_origin == QP2::point_origin)
       return lhs.quantity_ref_from(point_origin) <=> rhs.quantity_ref_from(QP2::point_origin);