diff --git a/docs/CHANGELOG.md b/docs/CHANGELOG.md
index ad028535..220030e1 100644
--- a/docs/CHANGELOG.md
+++ b/docs/CHANGELOG.md
@@ -1,6 +1,8 @@
 # Release notes
 
 - **0.8.0 WIP**
+  - (!) refactor: `common_quantity`, `common_quantity_for`, `common_quantity_point`, `common_quantity_kind`, and `common_quantity_point_kind` removed
+  - refactor: `quantity` `op+()` and `op-()` reimplemented in terms of `reference` rather then `quantity` types
   - (!) fix: add `quantity_point::origin`, like `std::chrono::time_point::clock`
   - fix: account for different dimensions in `quantity_point_cast`'s constraint
   - build: doxygen updated to 1.9.1
diff --git a/src/core/include/units/bits/common_quantity.h b/src/core/include/units/bits/common_type.h
similarity index 69%
rename from src/core/include/units/bits/common_quantity.h
rename to src/core/include/units/bits/common_type.h
index 789ff5b1..46940940 100644
--- a/src/core/include/units/bits/common_quantity.h
+++ b/src/core/include/units/bits/common_type.h
@@ -28,6 +28,9 @@
 
 namespace units {
 
+template<Dimension D, UnitOf<D> U>
+struct reference;
+
 template<Dimension D, UnitOf<D> U, Representation Rep>
 class quantity;
 
@@ -42,49 +45,42 @@ class quantity_point_kind;
 
 namespace detail {
 
-template<typename Q1, typename Q2, typename Rep>
-struct common_quantity_impl;
+template<typename R1, typename R2>
+struct common_quantity_reference_impl;
 
-template<typename D, typename U, typename Rep1, typename Rep2, typename Rep>
-struct common_quantity_impl<quantity<D, U, Rep1>, quantity<D, U, Rep2>, Rep> {
-  using type = quantity<D, U, Rep>;
+template<typename D, typename U>
+struct common_quantity_reference_impl<reference<D, U>, reference<D, U>> {
+  using type = reference<D, U>;
 };
 
-template<typename D, typename U1, typename Rep1, typename U2, typename Rep2, typename Rep>
-struct common_quantity_impl<quantity<D, U1, Rep1>, quantity<D, U2, Rep2>, Rep> {
-  using type = quantity<D, downcast_unit<D, common_ratio(U1::ratio, U2::ratio)>, Rep>;
+template<typename D, typename U1, typename U2>
+struct common_quantity_reference_impl<reference<D, U1>, reference<D, U2>> {
+  using type = reference<D, downcast_unit<D, common_ratio(U1::ratio, U2::ratio)>>;
 };
 
-template<typename D1, typename U1, typename Rep1, typename D2, typename U2, typename Rep2, typename Rep>
+template<typename D1, typename U1, typename D2, typename U2>
   requires same_unit_reference<dimension_unit<D1>, dimension_unit<D2>>::value
-struct common_quantity_impl<quantity<D1, U1, Rep1>, quantity<D2, U2, Rep2>, Rep> {
-  using type = quantity<D1, downcast_unit<D1, common_ratio(U1::ratio, U2::ratio)>, Rep>;
+struct common_quantity_reference_impl<reference<D1, U1>, reference<D2, U2>> {
+  using type = reference<D1, downcast_unit<D1, common_ratio(U1::ratio, U2::ratio)>>;
 };
 
-template<typename D1, typename U1, typename Rep1, typename D2, typename U2, typename Rep2, typename Rep>
-struct common_quantity_impl<quantity<D1, U1, Rep1>, quantity<D2, U2, Rep2>, Rep> {
+template<typename D1, typename U1, typename D2, typename U2>
+struct common_quantity_reference_impl<reference<D1, U1>, reference<D2, U2>> {
   using dimension = conditional<is_specialization_of<D1, unknown_dimension>, D2, D1>;
   static constexpr ratio r1 = D1::base_units_ratio * U1::ratio;
   static constexpr ratio r2 = D2::base_units_ratio * U2::ratio;
   static constexpr ratio cr = common_ratio(r1, r2);
   using unit = downcast_unit<dimension, cr / dimension::base_units_ratio>;
-  using type = quantity<dimension, unit, Rep>;
+  using type = reference<dimension, unit>;
 };
 
+
+template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
+using common_quantity_reference =
+  TYPENAME detail::common_quantity_reference_impl <
+  std::remove_const_t<decltype(Q1::reference)>, std::remove_const_t<decltype(Q2::reference)>>::type;
+
 }  // namespace detail
-
-template<Quantity Q1, QuantityEquivalentTo<Q1> Q2, Representation Rep = std::common_type_t<typename Q1::rep, typename Q2::rep>>
-using common_quantity = TYPENAME detail::common_quantity_impl<Q1, Q2, Rep>::type;
-
-template<QuantityPoint QP1, QuantityPointEquivalentTo<QP1> QP2>
-using common_quantity_point = std::common_type_t<QP1, QP2>;
-
-template<QuantityKind QK1, QuantityKindEquivalentTo<QK1> QK2>
-using common_quantity_kind = std::common_type_t<QK1, QK2>;
-
-template<QuantityPointKind QPK1, QuantityPointKindEquivalentTo<QPK1> QPK2>
-using common_quantity_point_kind = std::common_type_t<QPK1, QPK2>;
-
 }  // namespace units
 
 namespace std {
@@ -92,7 +88,10 @@ namespace std {
 template<units::Quantity Q1, units::QuantityEquivalentTo<Q1> Q2>
   requires requires { typename common_type_t<typename Q1::rep, typename Q2::rep>; }
 struct common_type<Q1, Q2> {
-  using type = units::common_quantity<Q1, Q2>;
+private:
+  using ref = units::detail::common_quantity_reference<Q1, Q2>;
+public:
+  using type = units::quantity<typename ref::dimension, typename ref::unit, common_type_t<typename Q1::rep, typename Q2::rep>>;
 };
 
 template<units::QuantityPoint QP1, units::QuantityPointEquivalentTo<QP1> QP2>
diff --git a/src/core/include/units/quantity.h b/src/core/include/units/quantity.h
index da3825a1..75d81d5f 100644
--- a/src/core/include/units/quantity.h
+++ b/src/core/include/units/quantity.h
@@ -23,7 +23,7 @@
 
 #pragma once
 
-#include <units/bits/common_quantity.h>
+#include <units/bits/common_type.h>
 #include <units/generic/dimensionless.h>
 
 // IWYU pragma: begin_exports
@@ -90,10 +90,6 @@ concept have_quantity_for_ =
   (!Quantity<V>) &&
   quantity_value_for_<Func, typename Q::rep, V>;
 
-template<typename Func, Quantity Q1, QuantityEquivalentTo<Q1> Q2>
-  requires quantity_value_for_<Func, typename Q1::rep, typename Q2::rep>
-using common_quantity_for = common_quantity<Q1, Q2, std::invoke_result_t<Func, typename Q1::rep, typename Q2::rep>>;
-
 template<QuantityLike Q>
 using quantity_like_type = quantity<typename quantity_like_traits<Q>::dimension, typename quantity_like_traits<Q>::unit, typename quantity_like_traits<Q>::rep>;
 
@@ -400,7 +396,8 @@ template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
   requires quantity_value_for_<std::plus<>, typename Q1::rep, typename Q2::rep>
 [[nodiscard]] constexpr Quantity auto operator+(const Q1& lhs, const Q2& rhs)
 {
-  using ret = common_quantity_for<std::plus<>, Q1, Q2>;
+  using ref = detail::common_quantity_reference<Q1, Q2>;
+  using ret = quantity<typename ref::dimension, typename ref::unit, decltype(lhs.number() + rhs.number())>;
   return ret(ret(lhs).number() + ret(rhs).number());
 }
 
@@ -408,7 +405,8 @@ template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
   requires quantity_value_for_<std::minus<>, typename Q1::rep, typename Q2::rep>
 [[nodiscard]] constexpr Quantity auto operator-(const Q1& lhs, const Q2& rhs)
 {
-  using ret = common_quantity_for<std::minus<>, Q1, Q2>;
+  using ref = detail::common_quantity_reference<Q1, Q2>;
+  using ret = quantity<typename ref::dimension, typename ref::unit, decltype(lhs.number() - rhs.number())>;
   return ret(ret(lhs).number() - ret(rhs).number());
 }
 
@@ -442,7 +440,7 @@ template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
   requires std::three_way_comparable_with<typename Q1::rep, typename Q2::rep>
 [[nodiscard]] constexpr auto operator<=>(const Q1& lhs, const Q2& rhs)
 {
-  using cq = common_quantity<Q1, Q2>;
+  using cq = std::common_type_t<Q1, Q2>;
   return cq(lhs).number() <=> cq(rhs).number();
 }
 
@@ -450,7 +448,7 @@ template<Quantity Q1, QuantityEquivalentTo<Q1> Q2>
   requires std::equality_comparable_with<typename Q1::rep, typename Q2::rep>
 [[nodiscard]] constexpr bool operator==(const Q1& lhs, const Q2& rhs)
 {
-  using cq = common_quantity<Q1, Q2>;
+  using cq = std::common_type_t<Q1, Q2>;
   return cq(lhs).number() == cq(rhs).number();
 }
 
diff --git a/test/unit_test/static/quantity_point_test.cpp b/test/unit_test/static/quantity_point_test.cpp
index d8e810d9..19b6e32f 100644
--- a/test/unit_test/static/quantity_point_test.cpp
+++ b/test/unit_test/static/quantity_point_test.cpp
@@ -22,7 +22,7 @@
 
 #include <units/quantity_point.h>
 #include "test_tools.h"
-#include <units/bits/common_quantity.h>
+#include <units/bits/common_type.h>
 #include <units/bits/external/type_traits.h>
 #include <units/chrono.h>
 #include <units/isq/si/length.h>
@@ -233,17 +233,17 @@ static_assert(2_q_dm3 + quantity_point(2_q_cm3) == quantity_point(2002_q_ml));
 
 static_assert(QuantityPoint<quantity_point<dynamic_origin<dim_length>, millimetre, int>>);
 
-// common_quantity_point
+// common_type
 
-static_assert(compare<
-              common_quantity_point<quantity_point<dynamic_origin<dim_length>, metre, int>, quantity_point<dynamic_origin<dim_length>, kilometre, int>>,
-              quantity_point<dynamic_origin<dim_length>, metre, int>>);
-static_assert(compare<common_quantity_point<quantity_point<dynamic_origin<dim_length>, kilometre, long long>,
-                                                   quantity_point<dynamic_origin<dim_length>, metre, int>>,
-                             quantity_point<dynamic_origin<dim_length>, metre, long long>>);
-static_assert(compare<common_quantity_point<quantity_point<dynamic_origin<dim_length>, kilometre, long long>,
-                                                   quantity_point<dynamic_origin<dim_length>, millimetre, double>>,
-                             quantity_point<dynamic_origin<dim_length>, millimetre, double>>);
+static_assert(compare<std::common_type_t<quantity_point<dynamic_origin<dim_length>, metre, int>,
+                                         quantity_point<dynamic_origin<dim_length>, kilometre, int>>,
+                      quantity_point<dynamic_origin<dim_length>, metre, int>>);
+static_assert(compare<std::common_type_t<quantity_point<dynamic_origin<dim_length>, kilometre, long long>,
+                                         quantity_point<dynamic_origin<dim_length>, metre, int>>,
+                      quantity_point<dynamic_origin<dim_length>, metre, long long>>);
+static_assert(compare<std::common_type_t<quantity_point<dynamic_origin<dim_length>, kilometre, long long>,
+                                         quantity_point<dynamic_origin<dim_length>, millimetre, double>>,
+                      quantity_point<dynamic_origin<dim_length>, millimetre, double>>);
 
 // common_type