diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index f17e7f5ec1..66822bd07f 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -27,6 +27,7 @@ jobs:
         - ["3.8",   "py38"]
         - ["3.9",   "py39"]
         - ["3.10",  "py310"]
+        - ["3.11.0-beta.5",  "py311"]
         - ["3.9",   "docs"]
         - ["3.9",   "coverage"]
         exclude:
@@ -35,6 +36,7 @@ jobs:
           - { os: windows, config: ["3.9",   "coverage"] }
 
     runs-on: ${{ matrix.os }}-latest
+    if: github.event_name != 'pull_request' || github.event.pull_request.head.repo.full_name != github.event.pull_request.base.repo.full_name
     name: ${{ matrix.os }}-${{ matrix.config[1] }}
     steps:
     - uses: actions/checkout@v2
@@ -59,7 +61,7 @@ jobs:
     - name: Coverage
       if: matrix.config[1] == 'coverage'
       run: |
-        pip install coveralls coverage-python-version
+        pip install coveralls
         coveralls --service=github
       env:
         GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
diff --git a/.meta.toml b/.meta.toml
index 1585d209d3..1338d83a49 100644
--- a/.meta.toml
+++ b/.meta.toml
@@ -2,7 +2,7 @@
 # https://github.com/zopefoundation/meta/tree/master/config/zope-product
 [meta]
 template = "zope-product"
-commit-id = "387516cfda91ee38cde868ef0d6205314a6a9bef"
+commit-id = "4689333adccd5ee16eda132085f840cc33248b57"
 
 [python]
 with-pypy = false
@@ -10,7 +10,7 @@ with-legacy-python = false
 with-docs = true
 with-sphinx-doctests = false
 with-windows = true
-with-future-python = false
+with-future-python = true
 
 [coverage]
 fail-under = 80
diff --git a/CHANGES.rst b/CHANGES.rst
index f7ce6be6d3..314fe65273 100644
--- a/CHANGES.rst
+++ b/CHANGES.rst
@@ -7,13 +7,15 @@ since the branch point at Zope 4.1.2.
 The change log for the previous version, Zope 4, is at
 https://github.com/zopefoundation/Zope/blob/4.x/CHANGES.rst
 
-5.5.3 (unreleased)
-------------------
+5.6 (unreleased)
+----------------
 
 - Make Products.PageTemplate engine compatible with Chameleon 3.10.
 
 - Update to newest compatible versions of dependencies.
 
+- Add preliminary support for Python 3.11 (as of 3.11.0b5).
+
 - Fix cookie path parameter handling:
   If the cookie path value contains ``%`` it is assumed to be
   fully quoted and used as is;
diff --git a/buildout.cfg b/buildout.cfg
index aebf58e9b2..97c790800e 100644
--- a/buildout.cfg
+++ b/buildout.cfg
@@ -18,7 +18,6 @@ parts =
 sources-dir = develop
 auto-checkout =
 
-
 [testenv]
 PYTHONHASHSEED = random
 
diff --git a/constraints.txt b/constraints.txt
index b8e558cedf..b9552f7d0c 100644
--- a/constraints.txt
+++ b/constraints.txt
@@ -12,9 +12,14 @@ Paste==3.5.1
 PasteDeploy==2.1.1
 Persistence==3.3
 Products.BTreeFolder2==4.3
-Products.ZCatalog==6.2
+Products.ZCatalog==6.3
 Record==3.5
-RestrictedPython==5.2
+RestrictedPython==5.2; python_version == '3.10'
+RestrictedPython==5.2; python_version == '3.6'
+RestrictedPython==5.2; python_version == '3.7'
+RestrictedPython==5.2; python_version == '3.8'
+RestrictedPython==5.2; python_version == '3.9'
+RestrictedPython==6.0a1.dev0; python_version > '3.10'
 SecretStorage==3.3.2
 WSGIProxy2==0.5.1
 WebOb==1.8.7
@@ -55,7 +60,7 @@ zope.cachedescriptors==4.3.1
 zope.component==5.0.1
 zope.componentvocabulary==2.3.0
 zope.configuration==4.4.1
-zope.container==4.5.0
+zope.container==4.6
 zope.contentprovider==4.2.1
 zope.contenttype==4.5.0
 zope.datetime==4.3.0
diff --git a/requirements-full.txt b/requirements-full.txt
index 8c95908153..307a2ba248 100644
--- a/requirements-full.txt
+++ b/requirements-full.txt
@@ -13,9 +13,14 @@ Paste==3.5.1
 PasteDeploy==2.1.1
 Persistence==3.3
 Products.BTreeFolder2==4.3
-Products.ZCatalog==6.2
+Products.ZCatalog==6.3
 Record==3.5
-RestrictedPython==5.2
+RestrictedPython==5.2; python_version == '3.10'
+RestrictedPython==5.2; python_version == '3.6'
+RestrictedPython==5.2; python_version == '3.7'
+RestrictedPython==5.2; python_version == '3.8'
+RestrictedPython==5.2; python_version == '3.9'
+RestrictedPython==6.0a1.dev0; python_version > '3.10'
 SecretStorage==3.3.2
 WSGIProxy2==0.5.1
 WebOb==1.8.7
@@ -56,7 +61,7 @@ zope.cachedescriptors==4.3.1
 zope.component==5.0.1
 zope.componentvocabulary==2.3.0
 zope.configuration==4.4.1
-zope.container==4.5.0
+zope.container==4.6
 zope.contentprovider==4.2.1
 zope.contenttype==4.5.0
 zope.datetime==4.3.0
diff --git a/setup.py b/setup.py
index 0d2c776b13..ad0a8ee3a3 100644
--- a/setup.py
+++ b/setup.py
@@ -29,8 +29,7 @@ def _read_file(filename):
 README = _read_file('README.rst')
 CHANGES = _read_file('CHANGES.rst')
 
-version = '5.5.3.dev0'
-
+version = '5.6.dev0'
 
 setup(
     name='Zope',
diff --git a/sources.cfg b/sources.cfg
index bce9652678..e9484e3499 100644
--- a/sources.cfg
+++ b/sources.cfg
@@ -31,6 +31,7 @@ Products.SiteErrorLog = git ${remotes:github}/Products.SiteErrorLog pushurl=${re
 Record = git ${remotes:github}/Record pushurl=${remotes:github_push}/Record
 
 # ZTK
+zodbpickle = git ${remotes:github}/zodbpickle
 zope.annotation = git ${remotes:github}/zope.annotation
 zope.browser = git ${remotes:github}/zope.browser
 zope.browsermenu = git ${remotes:github}/zope.browsermenu
diff --git a/tox.ini b/tox.ini
index 7922c3f2d4..4679be6cdf 100644
--- a/tox.ini
+++ b/tox.ini
@@ -9,6 +9,7 @@ envlist =
     py38
     py39
     py310
+    py311
     docs
     coverage
     pre-commit
@@ -92,7 +93,6 @@ allowlist_externals =
 deps =
     {[testenv]deps}
     coverage
-    coverage-python-version
 commands =
     mkdir -p {toxinidir}/parts/htmlcov
     coverage run {envdir}/bin/alltests {posargs:-vc}
@@ -101,7 +101,6 @@ commands =
 
 [coverage:run]
 branch = True
-plugins = coverage_python_version
 source = src
 
 [coverage:report]
diff --git a/util.py b/util.py
index 5da828ff3d..739a027b19 100644
--- a/util.py
+++ b/util.py
@@ -1,5 +1,6 @@
 import os
 from typing import Optional, Tuple, List
+from configparser import NoSectionError
 from configparser import RawConfigParser
 
 
@@ -24,9 +25,17 @@ def generate(in_, requirements_file, constraints_file):
     constraints = []
     zope_requirement = (
         '-e git+https://github.com/zopefoundation/Zope.git@master#egg=Zope\n')
-    zope_requirement = _generate(
-        parser.items('versions:python36'), '3.6', requirements, constraints,
-        zope_requirement)
+
+    # Try to include sections for all currently supported Python versions
+    for py_version in ('3.6', '3.7', '3.8', '3.9', '3.10', '3.11'):
+        short_version = py_version.replace('.', '')
+        try:
+            zope_requirement = _generate(
+                parser.items(f'versions:python{short_version}'), py_version,
+                requirements, constraints, zope_requirement)
+        except NoSectionError:
+            continue
+
     # "Unversioned" pins must come last, how they are handled depends on
     # Python version qualifiers for dependencies of the same name.
     zope_requirement = _generate(
@@ -51,7 +60,7 @@ def _generate(
 ) -> str:
     """Generate requirements and constraints for a specific Python version.
 
-    If ``python_version`` is falsy, generate for all python versions.
+    If ``python_version`` is false, generate for all python versions.
     Returns a probably changed ``zope_requirement``.
     """
     global PYTHON_VERSIONED
@@ -74,7 +83,8 @@ def _generate(
             PYTHON_VERSIONED[name] = versions
         else:
             if name in PYTHON_VERSIONED:
-                versions = sorted(PYTHON_VERSIONED.get(name))
+                versions = sorted(PYTHON_VERSIONED.get(name),
+                                  key=lambda s: list(map(int, s.split('.'))))
                 spec = f"{spec}; python_version > '{versions[-1]}'"
 
         requirements.append(spec + '\n')
diff --git a/versions-prod.cfg b/versions-prod.cfg
index 2d003efe00..6ba47326d6 100644
--- a/versions-prod.cfg
+++ b/versions-prod.cfg
@@ -20,7 +20,7 @@ Persistence = 3.3
 Products.BTreeFolder2 = 4.3
 Products.ZCatalog = 6.3
 Record = 3.5
-RestrictedPython = 5.2
+RestrictedPython = 6.0a1.dev0
 SecretStorage = 3.3.2
 WSGIProxy2 = 0.5.1
 WebOb = 1.8.7
@@ -58,7 +58,7 @@ zope.cachedescriptors = 4.3.1
 zope.component = 5.0.1
 zope.componentvocabulary = 2.3.0
 zope.configuration = 4.4.1
-zope.container = 4.5.0
+zope.container = 4.6
 zope.contentprovider = 4.2.1
 zope.contenttype = 4.5.0
 zope.datetime = 4.3.0
@@ -100,3 +100,16 @@ zope.viewlet = 4.3
 [versions:python36]
 jeepney = 0.7.1
 waitress = 2.0.0
+RestrictedPython = 5.2
+
+[versions:python37]
+RestrictedPython = 5.2
+
+[versions:python38]
+RestrictedPython = 5.2
+
+[versions:python39]
+RestrictedPython = 5.2
+
+[versions:python310]
+RestrictedPython = 5.2
diff --git a/versions.cfg b/versions.cfg
index 21f914871a..a92a3eca07 100644
--- a/versions.cfg
+++ b/versions.cfg
@@ -21,8 +21,10 @@ docutils = 0.17.1
 idna = 3.3
 imagesize = 1.3.0
 mr.developer = 2.0.1
+packaging = 21.3
 plone.recipe.command = 1.1
 pycparser = 2.21
+pyparsing = 3.0.7
 python-gettext = 4.0
 requests = 2.28.1
 snowballstemmer = 2.2.0