diff --git a/.github/workflows/release.yaml b/.github/workflows/release.yaml
index 9d4b1fd..1dd9303 100644
--- a/.github/workflows/release.yaml
+++ b/.github/workflows/release.yaml
@@ -39,15 +39,15 @@ jobs:
 
           Includes:
           * Python ${{ env.PY_VERSION }}.?
-          * OpenSSL 3.0.5
+          * OpenSSL 3.1.2
           * BZip2 1.0.8
-          * XZ 5.2.6
-          * LibFFI 3.4.2
+          * XZ 5.4.4
+          * LibFFI 3.4.4
     outputs:
       upload_url: ${{ steps.create_release.outputs.upload_url }}
 
   build:
-    runs-on: macOS-12
+    runs-on: macOS-latest
     needs: make-release
     strategy:
       max-parallel: 4
diff --git a/Makefile b/Makefile
index b7f2d29..502ef9b 100644
--- a/Makefile
+++ b/Makefile
@@ -65,7 +65,7 @@ CURL_FLAGS=--disable --fail --location --create-dirs --progress-bar
 
 # macOS targets
 TARGETS-macOS=macosx.x86_64 macosx.arm64
-VERSION_MIN-macOS=10.15
+VERSION_MIN-macOS=11.0
 CFLAGS-macOS=-mmacosx-version-min=$(VERSION_MIN-macOS)
 
 # iOS targets
@@ -847,6 +847,7 @@ $$(PYTHON_SRCDIR-$(sdk))/Makefile: \
 			LIBLZMA_LIBS="-L$$(XZ_MERGE-$(sdk))/lib -llzma" \
 			BZIP2_CFLAGS="-I$$(BZIP2_MERGE-$(sdk))/include" \
 			BZIP2_LIBS="-L$$(BZIP2_MERGE-$(sdk))/lib -lbz2" \
+			MACOSX_DEPLOYMENT_TARGET="$$(VERSION_MIN-$(os))" \
 			--prefix="$$(PYTHON_INSTALL-$(sdk))" \
 			--enable-ipv6 \
 			--enable-universalsdk \
diff --git a/README.rst b/README.rst
index 87a9b9c..aa946c1 100644
--- a/README.rst
+++ b/README.rst
@@ -4,7 +4,7 @@ Python Apple Support
 This is a meta-package for building a version of Python that can be embedded
 into a macOS, iOS, tvOS or watchOS project.
 
-**This branch builds a packaged version of Python 3.11.5**.
+**This branch builds a packaged version of Python 3.11.6**.
 Other Python versions are available by cloning other branches of the main
 repository:
 
@@ -12,6 +12,7 @@ repository:
 * `Python 3.9 <https://github.com/beeware/Python-Apple-support/tree/3.9>`__
 * `Python 3.10 <https://github.com/beeware/Python-Apple-support/tree/3.10>`__
 * `Python 3.12 <https://github.com/beeware/Python-Apple-support/tree/3.12>`__
+* `Python 3.13 <https://github.com/beeware/Python-Apple-support/tree/3.13>`__
 
 It works by downloading, patching, and building a fat binary of Python and selected
 pre-requisites, and packaging them as static libraries that can be incorporated into an
@@ -41,10 +42,10 @@ The binaries support x86_64 and arm64 for macOS; arm64 for iOS and appleTV
 devices; and arm64_32 for watchOS. It also supports device simulators on both
 x86_64 and M1 hardware. This should enable the code to run on:
 
-* macOS 10.15 (Catalina) or later, on:
+* macOS 11 (Big Sur) or later, on:
     * MacBook (including MacBooks using Apple Silicon)
     * iMac (including iMacs using Apple Silicon)
-    * Mac Mini (including M1 Apple Silicon Mac minis)
+    * Mac Mini (including Apple Silicon Mac minis)
     * Mac Studio (all models)
     * Mac Pro (all models)
 * iOS 12.0 or later, on:
diff --git a/patch/Python/Python.patch b/patch/Python/Python.patch
index 0cd550b..833df31 100644
--- a/patch/Python/Python.patch
+++ b/patch/Python/Python.patch
@@ -131,7 +131,7 @@ index 2ce5c5b64d..6e10a0c4a5 100644
              import pwd
              os.environ['HOME'] = pwd.getpwuid(os.getuid())[5]
 diff --git a/Lib/importlib/_bootstrap_external.py b/Lib/importlib/_bootstrap_external.py
-index f603a89f7f..48463efcfc 100644
+index f603a89f7f..92af10f21a 100644
 --- a/Lib/importlib/_bootstrap_external.py
 +++ b/Lib/importlib/_bootstrap_external.py
 @@ -52,7 +52,7 @@
@@ -143,7 +143,7 @@ index f603a89f7f..48463efcfc 100644
  _CASE_INSENSITIVE_PLATFORMS =  (_CASE_INSENSITIVE_PLATFORMS_BYTES_KEY
                                  + _CASE_INSENSITIVE_PLATFORMS_STR_KEY)
  
-@@ -1705,6 +1705,60 @@
+@@ -1705,6 +1705,59 @@
          return 'FileFinder({!r})'.format(self.path)
  
  
@@ -190,10 +190,9 @@ index f603a89f7f..48463efcfc 100644
 +
 +    def find_spec(self, fullname, path, target=None):
 +        name = fullname.split(".")[-1]
-+        framework_name = "_".join(fullname.split("."))
 +
 +        for extension in EXTENSION_SUFFIXES:
-+            dylib_file = _path_join(self.frameworks_path, f"{framework_name}.framework", f"{name}{extension}")
++            dylib_file = _path_join(self.frameworks_path, f"{fullname}.framework", f"{name}{extension}")
 +            _bootstrap._verbose_message('Looking for Apple Framework dylib {}', dylib_file)
 +            if _path_isfile(dylib_file):
 +                loader = AppleFrameworkLoader(fullname, dylib_file, path)
@@ -204,7 +203,7 @@ index f603a89f7f..48463efcfc 100644
  # Import setup ###############################################################
  
  def _fix_up_module(ns, name, pathname, cpathname=None):
-@@ -1752,3 +1806,7 @@
+@@ -1752,3 +1805,7 @@
      supported_loaders = _get_supported_file_loaders()
      sys.path_hooks.extend([FileFinder.path_hook(*supported_loaders)])
      sys.meta_path.append(PathFinder)