diff --git a/tests/allheaders.cpp b/tests/allheaders.cpp
index 5f3e4a94c6..510f858495 100644
--- a/tests/allheaders.cpp
+++ b/tests/allheaders.cpp
@@ -10,8 +10,392 @@
 // headers
 // ----------------------------------------------------------------------------
 
+// Note: can't use wxCHECK_GCC_VERSION() here as it's not defined yet.
+#if defined(__GNUC__)
+    #define CHECK_GCC_VERSION(major, minor) \
+      (__GNUC__ > (major) || (__GNUC__ == (major) && __GNUC_MINOR__ >= (minor)))
+#else
+    #define CHECK_GCC_VERSION(major, minor) 0
+#endif
+
+#if CHECK_GCC_VERSION(4, 6)
+    // As above, we can't reuse wxCONCAT() and wxSTRINGIZE macros from wx/cpp.h
+    // here, so define their equivalents here.
+    #define CONCAT_HELPER(x, y) x ## y
+    #define CONCAT(x1, x2)      CONCAT_HELPER(x1, x2)
+
+    #define STRINGIZE_HELPER(x) #x
+    #define STRINGIZE(x)        STRINGIZE_HELPER(x)
+
+    #define GCC_TURN_ON(warn) \
+        _Pragma(STRINGIZE(GCC diagnostic error STRINGIZE(CONCAT(-W,warn))))
+    #define GCC_TURN_OFF(warn) \
+        _Pragma(STRINGIZE(GCC diagnostic ignored STRINGIZE(CONCAT(-W,warn))))
+#endif
+
+// Due to what looks like a bug in gcc, some warnings enabled after including
+// the standard headers still result in warnings being given when instantiating
+// some functions defined in these headers later and we need to explicitly
+// disable these warnings to avoid them, even if they're not enabled yet.
+#ifdef GCC_TURN_OFF
+    #pragma GCC diagnostic push
+
+    GCC_TURN_OFF(aggregate-return)
+    GCC_TURN_OFF(conversion)
+    GCC_TURN_OFF(padded)
+    GCC_TURN_OFF(parentheses)
+    GCC_TURN_OFF(sign-compare)
+    GCC_TURN_OFF(sign-conversion)
+    GCC_TURN_OFF(unused-parameter)
+    GCC_TURN_OFF(zero-as-null-pointer-constant)
+#endif
+
+// We have to include this one first in order to check for HAVE_XXX below.
 #include "wx/setup.h"
 
+// Include all standard headers that are used in wx headers before enabling the
+// warnings below.
+#include <algorithm>
+#include <cmath>
+#include <exception>
+#include <functional>
+#include <iomanip>
+#include <iostream>
+#include <list>
+#include <locale>
+#include <map>
+#include <set>
+#include <sstream>
+#include <string>
+#include <vector>
+
+#if defined(HAVE_STD_UNORDERED_MAP)
+    #include <unordered_map>
+#endif
+#if defined(HAVE_STD_UNORDERED_SET)
+    #include <unordered_set>
+#endif
+
+#if defined(HAVE_DLOPEN)
+    #include <dlfcn.h>
+#endif
+#include <fcntl.h>
+
+#include "catch.hpp"
+
+#ifdef GCC_TURN_OFF
+    #pragma GCC diagnostic pop
+#endif
+
+// Enable max warning level for headers if possible, using gcc pragmas.
+#ifdef GCC_TURN_ON
+    // Enable all the usual "maximal" warnings.
+    GCC_TURN_ON(all)
+    GCC_TURN_ON(extra)
+    GCC_TURN_ON(pedantic)
+
+    // Enable all the individual warnings not enabled by one of the warnings
+    // above.
+
+    // Start of semi-auto-generated part, don't modify it manually.
+    //
+    // Manual changes:
+    //  - Globally replace HANDLE_GCC_WARNING with GCC_TURN_ON.
+    //  - Add v6 check for -Wabi, gcc < 6 don't seem to support turning it off
+    //    once it's turned on and gives it for the standard library symbols.
+    // {{{
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(abi)
+#endif // 6.1
+#if CHECK_GCC_VERSION(4,8)
+    GCC_TURN_ON(abi-tag)
+#endif // 4.8
+    GCC_TURN_ON(address)
+    GCC_TURN_ON(aggregate-return)
+#if CHECK_GCC_VERSION(7,1)
+    GCC_TURN_ON(alloc-zero)
+#endif // 7.1
+#if CHECK_GCC_VERSION(7,1)
+    GCC_TURN_ON(alloca)
+#endif // 7.1
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_ON(arith-conversion)
+#endif // 10.1
+    GCC_TURN_ON(array-bounds)
+    GCC_TURN_ON(builtin-macro-redefined)
+    GCC_TURN_ON(cast-align)
+#if CHECK_GCC_VERSION(8,1)
+    GCC_TURN_ON(cast-align=strict)
+#endif // 8.1
+    GCC_TURN_ON(cast-qual)
+    GCC_TURN_ON(char-subscripts)
+#if CHECK_GCC_VERSION(9,1)
+    GCC_TURN_ON(chkp)
+#endif // 9.1
+#if CHECK_GCC_VERSION(8,1)
+    GCC_TURN_ON(class-memaccess)
+#endif // 8.1
+    GCC_TURN_ON(clobbered)
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_ON(comma-subscript)
+#endif // 10.1
+    GCC_TURN_ON(comment)
+#if CHECK_GCC_VERSION(4,9)
+    GCC_TURN_ON(conditionally-supported)
+#endif // 4.9
+    GCC_TURN_ON(conversion)
+    GCC_TURN_ON(ctor-dtor-privacy)
+#if CHECK_GCC_VERSION(4,9)
+    GCC_TURN_ON(date-time)
+#endif // 4.9
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(delete-non-virtual-dtor)
+#endif // 4.7
+#if CHECK_GCC_VERSION(9,1)
+    GCC_TURN_ON(deprecated-copy)
+#endif // 9.1
+#if CHECK_GCC_VERSION(9,1)
+    GCC_TURN_ON(deprecated-copy-dtor)
+#endif // 9.1
+    GCC_TURN_ON(disabled-optimization)
+    GCC_TURN_ON(double-promotion)
+#if CHECK_GCC_VERSION(7,1)
+    GCC_TURN_ON(duplicated-branches)
+#endif // 7.1
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(duplicated-cond)
+#endif // 6.1
+    GCC_TURN_ON(empty-body)
+    GCC_TURN_ON(endif-labels)
+    GCC_TURN_ON(enum-compare)
+#if CHECK_GCC_VERSION(8,1)
+    GCC_TURN_ON(extra-semi)
+#endif // 8.1
+    GCC_TURN_ON(float-equal)
+    GCC_TURN_ON(format)
+    GCC_TURN_ON(format-contains-nul)
+    GCC_TURN_ON(format-extra-args)
+    GCC_TURN_ON(format-nonliteral)
+    GCC_TURN_ON(format-security)
+#if CHECK_GCC_VERSION(5,1)
+    GCC_TURN_ON(format-signedness)
+#endif // 5.1
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(format-zero-length)
+#endif // 4.7
+    GCC_TURN_ON(ignored-qualifiers)
+    GCC_TURN_ON(init-self)
+    GCC_TURN_ON(inline)
+    GCC_TURN_ON(invalid-pch)
+#if CHECK_GCC_VERSION(4,8)
+    GCC_TURN_ON(literal-suffix)
+#endif // 4.8
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(logical-op)
+#endif // 6.1
+    GCC_TURN_ON(long-long)
+    GCC_TURN_ON(main)
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(maybe-uninitialized)
+#endif // 4.7
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_ON(mismatched-tags)
+#endif // 10.1
+    GCC_TURN_ON(missing-braces)
+    GCC_TURN_ON(missing-declarations)
+    GCC_TURN_ON(missing-field-initializers)
+    GCC_TURN_ON(missing-format-attribute)
+    GCC_TURN_ON(missing-include-dirs)
+    GCC_TURN_ON(missing-noreturn)
+    GCC_TURN_ON(multichar)
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(namespaces)
+#endif // 6.1
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(narrowing)
+#endif // 4.7
+    GCC_TURN_ON(noexcept)
+#if CHECK_GCC_VERSION(7,1)
+    GCC_TURN_ON(noexcept-type)
+#endif // 7.1
+    GCC_TURN_ON(non-virtual-dtor)
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(nonnull)
+#endif // 4.7
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(null-dereference)
+#endif // 6.1
+    GCC_TURN_ON(old-style-cast)
+    GCC_TURN_ON(overlength-strings)
+    GCC_TURN_ON(overloaded-virtual)
+    GCC_TURN_ON(packed)
+    GCC_TURN_ON(packed-bitfield-compat)
+    GCC_TURN_ON(padded)
+    GCC_TURN_ON(parentheses)
+#if CHECK_GCC_VERSION(9,1)
+    GCC_TURN_ON(pessimizing-move)
+#endif // 9.1
+    GCC_TURN_ON(pointer-arith)
+    GCC_TURN_ON(redundant-decls)
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_ON(redundant-tags)
+#endif // 10.1
+#if CHECK_GCC_VERSION(7,1)
+    GCC_TURN_ON(register)
+#endif // 7.1
+    GCC_TURN_ON(reorder)
+#if CHECK_GCC_VERSION(7,1)
+    GCC_TURN_ON(restrict)
+#endif // 7.1
+    GCC_TURN_ON(return-type)
+    GCC_TURN_ON(sequence-point)
+    GCC_TURN_ON(shadow)
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(shift-negative-value)
+#endif // 6.1
+    GCC_TURN_ON(sign-compare)
+    GCC_TURN_ON(sign-conversion)
+    GCC_TURN_ON(sign-promo)
+    GCC_TURN_ON(stack-protector)
+    GCC_TURN_ON(strict-aliasing)
+    GCC_TURN_ON(strict-null-sentinel)
+    GCC_TURN_ON(strict-overflow)
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_ON(string-compare)
+#endif // 10.1
+#if CHECK_GCC_VERSION(8,1)
+    GCC_TURN_ON(stringop-truncation)
+#endif // 8.1
+#if CHECK_GCC_VERSION(8,1)
+    GCC_TURN_ON(suggest-attribute=cold)
+#endif // 8.1
+    GCC_TURN_ON(suggest-attribute=const)
+#if CHECK_GCC_VERSION(4,8)
+    GCC_TURN_ON(suggest-attribute=format)
+#endif // 4.8
+#if CHECK_GCC_VERSION(8,1)
+    GCC_TURN_ON(suggest-attribute=malloc)
+#endif // 8.1
+    GCC_TURN_ON(suggest-attribute=noreturn)
+    GCC_TURN_ON(suggest-attribute=pure)
+#if CHECK_GCC_VERSION(5,1)
+    GCC_TURN_ON(suggest-final-methods)
+#endif // 5.1
+#if CHECK_GCC_VERSION(5,1)
+    GCC_TURN_ON(suggest-final-types)
+#endif // 5.1
+#if CHECK_GCC_VERSION(5,1)
+    GCC_TURN_ON(suggest-override)
+#endif // 5.1
+    GCC_TURN_ON(switch)
+    GCC_TURN_ON(switch-default)
+    GCC_TURN_ON(switch-enum)
+    GCC_TURN_ON(synth)
+    GCC_TURN_ON(system-headers)
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(templates)
+#endif // 6.1
+    GCC_TURN_ON(trampolines)
+    GCC_TURN_ON(trigraphs)
+    GCC_TURN_ON(type-limits)
+    GCC_TURN_ON(undef)
+    GCC_TURN_ON(uninitialized)
+    GCC_TURN_ON(unknown-pragmas)
+    GCC_TURN_ON(unreachable-code)
+    GCC_TURN_ON(unsafe-loop-optimizations)
+    GCC_TURN_ON(unused)
+    GCC_TURN_ON(unused-but-set-parameter)
+    GCC_TURN_ON(unused-but-set-variable)
+    GCC_TURN_ON(unused-function)
+    GCC_TURN_ON(unused-label)
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(unused-local-typedefs)
+#endif // 4.7
+    GCC_TURN_ON(unused-macros)
+    GCC_TURN_ON(unused-parameter)
+    GCC_TURN_ON(unused-value)
+    GCC_TURN_ON(unused-variable)
+#if CHECK_GCC_VERSION(4,8)
+    GCC_TURN_ON(useless-cast)
+#endif // 4.8
+    GCC_TURN_ON(variadic-macros)
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(vector-operation-performance)
+#endif // 4.7
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_ON(virtual-inheritance)
+#endif // 6.1
+    GCC_TURN_ON(vla)
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_ON(volatile)
+#endif // 10.1
+    GCC_TURN_ON(volatile-register-var)
+    GCC_TURN_ON(write-strings)
+#if CHECK_GCC_VERSION(4,7)
+    GCC_TURN_ON(zero-as-null-pointer-constant)
+#endif // 4.7
+    // }}}
+
+    #undef GCC_TURN_ON
+
+    /*
+        Some warnings still must be disabled, so turn them back off explicitly:
+    */
+
+    // Those are potentially useful warnings, but there are just too many
+    // occurrences of them in our code currently.
+    GCC_TURN_OFF(conversion)
+    GCC_TURN_OFF(sign-compare)
+    GCC_TURN_OFF(sign-conversion)
+
+    GCC_TURN_OFF(old-style-cast)
+#if CHECK_GCC_VERSION(4,8)
+    GCC_TURN_OFF(useless-cast)
+#endif // 4.8
+
+#if CHECK_GCC_VERSION(10,1)
+    GCC_TURN_OFF(redundant-tags) // "struct tm" triggers this
+#endif // 10.1
+
+    // This one is given for NULL, and not just literal 0, up to gcc 10, and so
+    // has to remain disabled for as long as we use any NULLs in our code.
+#if CHECK_GCC_VERSION(4,7) && !CHECK_GCC_VERSION(10,1)
+    GCC_TURN_OFF(zero-as-null-pointer-constant)
+#endif
+
+    // wxWARNING_SUPPRESS_MISSING_OVERRIDE() inside wxRTTI macros is just
+    // ignored by gcc up to 9.x for some reason, so we have no choice but to
+    // disable it.
+#if CHECK_GCC_VERSION(5,1) && !CHECK_GCC_VERSION(9,0)
+    GCC_TURN_OFF(suggest-override)
+#endif
+
+    // The rest are the warnings that we don't ever want to enable.
+
+    // This one is given whenever inheriting from std:: classes without using
+    // C++11 ABI tag explicitly, probably harmless.
+#if CHECK_GCC_VERSION(4,8)
+    GCC_TURN_OFF(abi-tag)
+#endif // 4.8
+
+    // All those are about using perfectly normal C++ features that are
+    // actually used in our code.
+    GCC_TURN_OFF(aggregate-return)
+    GCC_TURN_OFF(long-long)
+#if CHECK_GCC_VERSION(6,1)
+    GCC_TURN_OFF(namespaces)
+    GCC_TURN_OFF(multiple-inheritance)
+    GCC_TURN_OFF(templates)
+#endif // 6.1
+
+    // This warns about missing "default" label in exhaustive switches over
+    // enums, so it's completely useless.
+    GCC_TURN_OFF(switch-default)
+
+    // We don't care about padding being added to our structs.
+    GCC_TURN_OFF(padded)
+#endif // gcc >= 4.6
+
 #if !wxUSE_UTF8_LOCALE_ONLY
 #define wxNO_IMPLICIT_WXSTRING_ENCODING
 #endif
@@ -20,6 +404,11 @@
 
 #include "allheaders.h"
 
+#ifdef GCC_TURN_OFF
+    // Just using REQUIRE() below triggers -Wparentheses, so avoid it.
+    GCC_TURN_OFF(parentheses)
+#endif
+
 TEST_CASE("wxNO_IMPLICIT_WXSTRING_ENCODING", "[string]")
 {
     wxString s = wxASCII_STR("Hello, ASCII");