diff --git a/include/nlohmann/detail/output/output_adapters.hpp b/include/nlohmann/detail/output/output_adapters.hpp
index 6f2462685..1cad57b19 100644
--- a/include/nlohmann/detail/output/output_adapters.hpp
+++ b/include/nlohmann/detail/output/output_adapters.hpp
@@ -37,11 +37,11 @@ template<typename CharType>
 using output_adapter_t = std::shared_ptr<output_adapter_protocol<CharType>>;
 
 /// output adapter for byte vectors
-template<typename CharType>
+template<typename CharType, typename AllocatorType = std::allocator<CharType>>
 class output_vector_adapter : public output_adapter_protocol<CharType>
 {
   public:
-    explicit output_vector_adapter(std::vector<CharType>& vec) noexcept
+    explicit output_vector_adapter(std::vector<CharType, AllocatorType>& vec) noexcept
         : v(vec)
     {}
 
@@ -57,7 +57,7 @@ class output_vector_adapter : public output_adapter_protocol<CharType>
     }
 
   private:
-    std::vector<CharType>& v;
+    std::vector<CharType, AllocatorType>& v;
 };
 
 #ifndef JSON_NO_IO
@@ -114,8 +114,9 @@ template<typename CharType, typename StringType = std::basic_string<CharType>>
 class output_adapter
 {
   public:
-    output_adapter(std::vector<CharType>& vec)
-        : oa(std::make_shared<output_vector_adapter<CharType>>(vec)) {}
+    template<typename AllocatorType = std::allocator<CharType>>
+    output_adapter(std::vector<CharType, AllocatorType>& vec)
+        : oa(std::make_shared<output_vector_adapter<CharType, AllocatorType>>(vec)) {}
 
 #ifndef JSON_NO_IO
     output_adapter(std::basic_ostream<CharType>& s)
diff --git a/include/nlohmann/json.hpp b/include/nlohmann/json.hpp
index 86510b4a8..b0b1e1d3c 100644
--- a/include/nlohmann/json.hpp
+++ b/include/nlohmann/json.hpp
@@ -6009,6 +6009,9 @@ class basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-spec
         for (auto it = j.cbegin(); it != j.cend(); ++it)
         {
             m_value.object->operator[](it.key()) = it.value();
+#if JSON_DIAGNOSTICS
+            m_value.object->operator[](it.key()).m_parent = this;
+#endif
         }
     }
 
@@ -6069,6 +6072,9 @@ class basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-spec
         for (auto it = first; it != last; ++it)
         {
             m_value.object->operator[](it.key()) = it.value();
+#if JSON_DIAGNOSTICS
+            m_value.object->operator[](it.key()).m_parent = this;
+#endif
         }
     }
 
diff --git a/single_include/nlohmann/json.hpp b/single_include/nlohmann/json.hpp
index 610206761..862330ea0 100644
--- a/single_include/nlohmann/json.hpp
+++ b/single_include/nlohmann/json.hpp
@@ -13764,11 +13764,11 @@ template<typename CharType>
 using output_adapter_t = std::shared_ptr<output_adapter_protocol<CharType>>;
 
 /// output adapter for byte vectors
-template<typename CharType>
+template<typename CharType, typename AllocatorType = std::allocator<CharType>>
 class output_vector_adapter : public output_adapter_protocol<CharType>
 {
   public:
-    explicit output_vector_adapter(std::vector<CharType>& vec) noexcept
+    explicit output_vector_adapter(std::vector<CharType, AllocatorType>& vec) noexcept
         : v(vec)
     {}
 
@@ -13784,7 +13784,7 @@ class output_vector_adapter : public output_adapter_protocol<CharType>
     }
 
   private:
-    std::vector<CharType>& v;
+    std::vector<CharType, AllocatorType>& v;
 };
 
 #ifndef JSON_NO_IO
@@ -13841,8 +13841,9 @@ template<typename CharType, typename StringType = std::basic_string<CharType>>
 class output_adapter
 {
   public:
-    output_adapter(std::vector<CharType>& vec)
-        : oa(std::make_shared<output_vector_adapter<CharType>>(vec)) {}
+    template<typename AllocatorType = std::allocator<CharType>>
+    output_adapter(std::vector<CharType, AllocatorType>& vec)
+        : oa(std::make_shared<output_vector_adapter<CharType, AllocatorType>>(vec)) {}
 
 #ifndef JSON_NO_IO
     output_adapter(std::basic_ostream<CharType>& s)
@@ -24010,6 +24011,9 @@ class basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-spec
         for (auto it = j.cbegin(); it != j.cend(); ++it)
         {
             m_value.object->operator[](it.key()) = it.value();
+#if JSON_DIAGNOSTICS
+            m_value.object->operator[](it.key()).m_parent = this;
+#endif
         }
     }
 
@@ -24070,6 +24074,9 @@ class basic_json // NOLINT(cppcoreguidelines-special-member-functions,hicpp-spec
         for (auto it = first; it != last; ++it)
         {
             m_value.object->operator[](it.key()) = it.value();
+#if JSON_DIAGNOSTICS
+            m_value.object->operator[](it.key()).m_parent = this;
+#endif
         }
     }
 
diff --git a/test/src/unit-diagnostics.cpp b/test/src/unit-diagnostics.cpp
index d4bbf93aa..8e4f2ffc3 100644
--- a/test/src/unit-diagnostics.cpp
+++ b/test/src/unit-diagnostics.cpp
@@ -184,4 +184,54 @@ TEST_CASE("Better diagnostics")
         j["second"] = value;
         j2["something"] = j;
     }
+
+    SECTION("Regression test for issue #3007 - Parent pointers properly set when using update()")
+    {
+        // void update(const_reference j)
+        {
+            json j = json::object();
+
+            {
+                json j2 = json::object();
+                j2["one"] = 1;
+
+                j.update(j2);
+            }
+
+            // Must call operator[] on const element, otherwise m_parent gets updated.
+            auto const& constJ = j;
+            CHECK_THROWS_WITH_AS(constJ["one"].at(0), "[json.exception.type_error.304] (/one) cannot use at() with number", json::type_error);
+        }
+
+        // void update(const_iterator first, const_iterator last)
+        {
+            json j = json::object();
+
+            {
+                json j2 = json::object();
+                j2["one"] = 1;
+
+                j.update(j2.begin(), j2.end());
+            }
+
+            // Must call operator[] on const element, otherwise m_parent gets updated.
+            auto const& constJ = j;
+            CHECK_THROWS_WITH_AS(constJ["one"].at(0), "[json.exception.type_error.304] (/one) cannot use at() with number", json::type_error);
+        }
+
+        // Code from #3007 triggering unwanted assertion without fix to update().
+        {
+            json root = json::array();
+            json lower = json::object();
+
+            {
+                json lowest = json::object();
+                lowest["one"] = 1;
+
+                lower.update(lowest);
+            }
+
+            root.push_back(lower);
+        }
+    }
 }
diff --git a/test/src/unit-regression2.cpp b/test/src/unit-regression2.cpp
index 8d0175e9d..a42220e47 100644
--- a/test/src/unit-regression2.cpp
+++ b/test/src/unit-regression2.cpp
@@ -181,6 +181,13 @@ class sax_no_exception : public nlohmann::detail::json_sax_dom_parser<json>
 
 std::string* sax_no_exception::error_string = nullptr;
 
+/////////////////////////////////////////////////////////////////////
+// for #2982
+/////////////////////////////////////////////////////////////////////
+
+template<class T>
+class my_allocator : public std::allocator<T>
+{};
 
 TEST_CASE("regression tests 2")
 {
@@ -679,6 +686,15 @@ TEST_CASE("regression tests 2")
         test3[json::json_pointer(p)] = json::object();
         CHECK(test3.dump() == "{\"/root\":{}}");
     }
+
+    SECTION("issue #2982 - to_{binary format} does not provide a mechanism for specifying a custom allocator for the returned type")
+    {
+        std::vector<std::uint8_t, my_allocator<std::uint8_t>> my_vector;
+        json j = {1, 2, 3, 4};
+        json::to_cbor(j, my_vector);
+        json k = json::from_cbor(my_vector);
+        CHECK(j == k);
+    }
 }
 
 DOCTEST_CLANG_SUPPRESS_WARNING_POP