diff --git a/lib/galaxy/dependencies/dev-requirements.txt b/lib/galaxy/dependencies/dev-requirements.txt
index b1c32b66192e..7c1a2c541c93 100644
--- a/lib/galaxy/dependencies/dev-requirements.txt
+++ b/lib/galaxy/dependencies/dev-requirements.txt
@@ -37,7 +37,8 @@ exceptiongroup==1.1.3 ; python_version >= "3.7" and python_version < "3.11"
 filelock==3.12.2 ; python_version >= "3.7" and python_version < "3.13"
 fluent-logger==0.10.0 ; python_version >= "3.7" and python_version < "3.13"
 fonttools==4.38.0 ; python_version >= "3.7" and python_version < "3.13"
-frozenlist==1.3.3 ; python_version >= "3.7" and python_version < "3.13"
+frozenlist==1.3.3 ; python_version >= "3.7" and python_version < "3.8"
+frozenlist==1.4.0 ; python_version >= "3.8" and python_version < "3.13"
 future==0.18.3 ; python_version >= "3.7" and python_version < "3.13"
 galaxy-release-util==0.1.5 ; python_version >= "3.7" and python_version < "3.13"
 greenlet==2.0.2 ; python_version >= "3.7" and python_version < "3.13"
diff --git a/lib/galaxy/dependencies/pinned-requirements.txt b/lib/galaxy/dependencies/pinned-requirements.txt
index be81bc18101e..d8ebe957f3d2 100644
--- a/lib/galaxy/dependencies/pinned-requirements.txt
+++ b/lib/galaxy/dependencies/pinned-requirements.txt
@@ -68,7 +68,8 @@ exceptiongroup==1.1.3 ; python_version >= "3.7" and python_version < "3.11"
 fastapi-utils==0.2.1 ; python_version >= "3.7" and python_version < "3.13"
 fastapi==0.98.0 ; python_version >= "3.7" and python_version < "3.13"
 filelock==3.12.2 ; python_version >= "3.7" and python_version < "3.13"
-frozenlist==1.3.3 ; python_version >= "3.7" and python_version < "3.13"
+frozenlist==1.3.3 ; python_version >= "3.7" and python_version < "3.8"
+frozenlist==1.4.0 ; python_version >= "3.8" and python_version < "3.13"
 fs==2.4.16 ; python_version >= "3.7" and python_version < "3.13"
 fsspec==2023.1.0 ; python_version >= "3.7" and python_version < "3.13"
 future==0.18.3 ; python_version >= "3.7" and python_version < "3.13"
@@ -84,7 +85,8 @@ gunicorn==21.2.0 ; python_version >= "3.7" and python_version < "3.13"
 gxformat2==0.18.0 ; python_version >= "3.7" and python_version < "3.13"
 h11==0.14.0 ; python_version >= "3.7" and python_version < "3.13"
 h5grove==1.3.0 ; python_version >= "3.7" and python_version < "3.13"
-h5py==3.8.0 ; python_version >= "3.7" and python_version < "3.13"
+h5py==3.8.0 ; python_version >= "3.7" and python_version < "3.8"
+h5py==3.10.0 ; python_version >= "3.8" and python_version < "3.13"
 humanfriendly==10.0 ; python_version >= "3.7" and python_version < "3.13"
 idna==3.4 ; python_version >= "3.7" and python_version < "3.13"
 importlib-metadata==4.13.0 ; python_version >= "3.7" and python_version < "3.13"
diff --git a/lib/galaxy/dependencies/update.sh b/lib/galaxy/dependencies/update.sh
index c294d7652eef..133cf9e02b45 100755
--- a/lib/galaxy/dependencies/update.sh
+++ b/lib/galaxy/dependencies/update.sh
@@ -86,9 +86,13 @@ split_requirement () {
 }
 
 # For some packages there is no recent version that works on all Python versions
-# supported by Galaxy, so Poetry resorts to an old version that didn't have a
-# maximum Python version pin. Here we replace any such requirement with multiple
-# Python-version-specific requirements.
+# supported by Galaxy, so Poetry resorts to an old version. Here we replace any
+# such requirement with multiple Python-version-specific requirements.
+# Packages which specify a maximum Python version pin:
 split_requirement matplotlib
 split_requirement numpy
 split_requirement scipy
+# Packages that added Python 3.12 support in a release that doesn't support 3.7
+# any more (i.e. they can be removed from here when we drop Python 3.7 support):
+split_requirement frozenlist
+split_requirement h5py