diff --git a/constraints.txt b/constraints.txt
new file mode 100644
index 0000000000..039eb0db27
--- /dev/null
+++ b/constraints.txt
@@ -0,0 +1 @@
+cython<3
diff --git a/requirements-devel.txt b/requirements-devel.txt
index 9f60915fa8..c25c80eb5d 100644
--- a/requirements-devel.txt
+++ b/requirements-devel.txt
@@ -11,7 +11,7 @@ click==8.1.3
 codespell==2.2.4
 colorama==0.4.6
 coverage==7.2.5
-craft-archives==1.1.2
+craft-archives==1.1.3
 craft-cli==2.0.0
 craft-grammar==1.1.1
 craft-parts==1.21.1
diff --git a/requirements.txt b/requirements.txt
index ba4458dff1..7335675b4a 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -5,7 +5,7 @@ cffi==1.15.1
 chardet==5.1.0
 charset-normalizer==3.1.0
 click==8.1.3
-craft-archives==1.1.2
+craft-archives==1.1.3
 craft-cli==2.0.0
 craft-grammar==1.1.1
 craft-parts==1.21.1
@@ -51,7 +51,7 @@ python-dateutil==2.8.2
 python-debian==0.1.49
 pytz==2023.3
 pyxdg==0.28
-PyYAML==6.0
+PyYAML==6.0.1
 raven==6.10.0
 requests==2.31.0
 requests-toolbelt==1.0.0
diff --git a/patches/ctypes_init.diff b/snap/local/patches/python/ctypes_init.diff
similarity index 100%
rename from patches/ctypes_init.diff
rename to snap/local/patches/python/ctypes_init.diff
diff --git a/snap/snapcraft.yaml b/snap/snapcraft.yaml
index c2139c1089..b030615d69 100644
--- a/snap/snapcraft.yaml
+++ b/snap/snapcraft.yaml
@@ -123,7 +123,7 @@ parts:
 
       # Apply patches
       echo "Patching ctypes..."
-      patch -s -b "${PYTHON_PACKAGE_PATH}/${CTYPES_INIT}" "${SNAPCRAFT_PROJECT_DIR}/patches/ctypes_init.diff"
+      patch -s -b "${PYTHON_PACKAGE_PATH}/${CTYPES_INIT}" "${SNAPCRAFT_PROJECT_DIR}/snap/local/patches/python/ctypes_init.diff"
 
       # Save patches to allow rebuilding
       mkdir -p patched/ctypes
@@ -144,6 +144,8 @@ parts:
         # Limited to < 66 because we need `pkg_resources` and because `python-apt`
         # does not build with the latest.
         - setuptools<66
+    python-constraints:
+        - constraints.txt
     python-requirements:
         - requirements.txt
     organize:
diff --git a/tests/spread/core22/package-repo-archs/armhf.yaml b/tests/spread/core22/package-repo-archs/armhf.yaml
new file mode 100644
index 0000000000..de3376e9ee
--- /dev/null
+++ b/tests/spread/core22/package-repo-archs/armhf.yaml
@@ -0,0 +1,38 @@
+name: test-archs
+version: '1.0'
+summary: test package repos with different architectures
+description: test package repos with different architectures
+grade: stable
+confinement: strict
+base: core22
+architectures:
+  - build-on: amd64
+
+package-repositories:
+  # The repo that contains libpython3.11-minimal:armhf
+  - type: apt
+    formats: [deb]
+    architectures: [armhf]
+    components: [main]
+    suites: [jammy]
+    key-id: F23C5A6CF475977595C89F51BA6932366A755776
+    url: https://ppa.launchpadcontent.net/deadsnakes/ppa/ubuntu
+  # Also add the armhf arch for the "ports" repo, to fetch python's deps. We
+  # need to do this because the default archives don't have armhf.
+  - type: apt
+    architectures: [ armhf ]
+    components: [ main ]
+    suites: [ jammy, jammy-security, jammy-updates ]
+    key-id: F6ECB3762474EDA9D21B7022871920D1991BC93C
+    url: http://ports.ubuntu.com/ubuntu-ports
+
+parts:
+  mypart:
+    plugin: nil
+    build-packages:
+      - file
+    stage-packages:
+      - libpython3.11-minimal:armhf
+    override-build: |
+      file ${CRAFT_PART_INSTALL}/usr/lib/arm-linux-gnueabihf/libssl.so.3 | grep "ARM"
+      craftctl default
diff --git a/tests/spread/core22/package-repo-archs/i386.yaml b/tests/spread/core22/package-repo-archs/i386.yaml
new file mode 100644
index 0000000000..b2e99953f4
--- /dev/null
+++ b/tests/spread/core22/package-repo-archs/i386.yaml
@@ -0,0 +1,33 @@
+name: test-archs
+version: '1.0'
+summary: test package repos with different architectures
+description: test package repos with different architectures
+grade: stable
+confinement: strict
+base: core22
+architectures:
+  - build-on: amd64
+
+package-repositories:
+  # The repo that contains libpython3.11-minimal:i386
+  - type: apt
+    formats: [deb]
+    architectures: [i386]
+    components: [main]
+    suites: [jammy]
+    key-id: F23C5A6CF475977595C89F51BA6932366A755776
+    url: https://ppa.launchpadcontent.net/deadsnakes/ppa/ubuntu
+  # We don't need to add the i386 architecture for the official archives,
+  # because the host building this (amd64) is compatible so Snapcraft will add
+  # the i386 platform "globally".
+
+parts:
+  mypart:
+    plugin: nil
+    build-packages:
+      - file
+    stage-packages:
+      - libpython3.11-minimal:i386
+    override-build: |
+      file ${CRAFT_PART_INSTALL}/usr/lib/i386-linux-gnu/libssl.so.3 | grep "ELF 32-bit"
+      craftctl default
diff --git a/tests/spread/core22/package-repo-archs/task.yaml b/tests/spread/core22/package-repo-archs/task.yaml
new file mode 100644
index 0000000000..766587e9db
--- /dev/null
+++ b/tests/spread/core22/package-repo-archs/task.yaml
@@ -0,0 +1,19 @@
+summary: Test using package-repositories with different architectures on core22
+
+environment:
+  SNAP_ARCH/i386: i386
+  SNAP_ARCH/armhf: armhf
+  SNAPCRAFT_BUILD_ENVIRONMENT: ""
+
+restore: |
+  snapcraft clean
+
+execute: |
+  # The task works by copying one of the arch-specific yaml files as
+  # "snapcraft.yaml", and then building it.
+  rm -rf snap/
+  mkdir snap
+  cp "$SNAP_ARCH".yaml snap/snapcraft.yaml
+
+  # The part's build script does the checking.
+  snapcraft build --verbose --use-lxd