diff --git a/var/spack/repos/builtin/packages/py-matplotlib/package.py b/var/spack/repos/builtin/packages/py-matplotlib/package.py
index eb307e99f7e..8cbcc65deb7 100644
--- a/var/spack/repos/builtin/packages/py-matplotlib/package.py
+++ b/var/spack/repos/builtin/packages/py-matplotlib/package.py
@@ -26,6 +26,7 @@ class PyMatplotlib(PythonPackage):
     license("Apache-2.0")
     maintainers("adamjstewart", "rgommers")
 
+    version("3.10.0", sha256="b886d02a581b96704c9d1ffe55709e49b4d2d52709ccebc4be42db856e511278")
     version("3.9.4", sha256="1e00e8be7393cbdc6fedfa8a6fba02cf3e83814b285db1c60b906a023ba41bc3")
     version("3.9.3", sha256="cd5dbbc8e25cad5f706845c4d100e2c8b34691b412b93717ce38d8ae803bcfa5")
     version("3.9.2", sha256="96ab43906269ca64a6366934106fa01534454a69e471b7bf3d79083981aaab92")
@@ -140,6 +141,7 @@ class PyMatplotlib(PythonPackage):
     # https://matplotlib.org/stable/install/dependencies.html
     # Runtime dependencies
     # Mandatory dependencies
+    depends_on("python@3.10:", when="@3.10:", type=("build", "link", "run"))
     depends_on("python@3.9:", when="@3.8:", type=("build", "link", "run"))
     depends_on("python@3.8:", when="@3.6:", type=("build", "link", "run"))
     depends_on("python", type=("build", "link", "run"))
@@ -184,7 +186,7 @@ class PyMatplotlib(PythonPackage):
         depends_on("py-pyqt4@4.6:", when="backend=" + backend, type="run")
         depends_on("qt+gui", when="backend=" + backend, type="run")
     for backend in ["qt5agg", "qt5cairo"]:
-        depends_on("py-pyqt5", when="backend=" + backend, type="run")
+        depends_on("py-pyqt5@5.12:", when="backend=" + backend, type="run")
         depends_on("qt+gui", when="backend=" + backend, type="run")
     for backend in ["qtagg", "qtcairo"]:
         depends_on("py-pyqt6@6.1:", when="backend=" + backend, type="run")
@@ -238,6 +240,7 @@ class PyMatplotlib(PythonPackage):
     # Setup dependencies
     depends_on("py-meson-python@0.13.1:0.16", when="@3.9:", type="build")
     depends_on("ninja@1.8.2:", when="@3.9:", type="build")
+    depends_on("py-pybind11@2.13.2:", when="@3.10:", type=("build", "link"))
     depends_on("py-pybind11@2.6:", when="@3.7:", type=("build", "link"))
     depends_on("py-setuptools-scm@7:", when="@3.6:", type="build")
     depends_on("py-setuptools-scm@4:6", when="@3.5", type="build")
@@ -260,7 +263,8 @@ class PyMatplotlib(PythonPackage):
     conflicts("platform=linux", when="backend=macosx", msg=msg)
     conflicts("platform=windows", when="backend=macosx", msg=msg)
 
-    conflicts("^tk@8.6.0:8.6.1")
+    conflicts("tk@8.6.0:8.6.1")
+    conflicts("py-pybind11@2.13.3")
 
     # https://github.com/matplotlib/matplotlib/pull/21662
     patch("matplotlibrc.patch", when="@3.5.0")