diff --git a/var/spack/repos/builtin/packages/spectre/package.py b/var/spack/repos/builtin/packages/spectre/package.py
index fb0b095cf6..e148c7d84f 100644
--- a/var/spack/repos/builtin/packages/spectre/package.py
+++ b/var/spack/repos/builtin/packages/spectre/package.py
@@ -34,9 +34,15 @@ class Spectre(CMakePackage):
     version(
         "2024.04.12", sha256="2ca46e1c493225e9067546595b1bb234d8634de4974ba87a7b8f011e686b44b6"
     )
+    version(
+        "2024.03.19", sha256="42a25c8827b56268d9826239cde521491be19318d83785b35cd0265a9f6a1f7c"
+    )
     version(
         "2024.02.05", sha256="cf5c4da473d665d0cac0a32562b1b8e8c0f1a77eebca8c3171e52cdf3056fdb3"
     )
+    version(
+        "2023.12.08", sha256="662b4df6b6cdb097f9edcba869b3e05affeae485de8766ca66bf21399c39a9d8"
+    )
     version(
         "2023.10.11", sha256="f25d17bc80cc49ebdd81726326701fe9ecd2b6705d86e6e3d48d9e4a458c8aff"
     )
@@ -134,7 +140,7 @@ class Spectre(CMakePackage):
         ),
         description="Executables to install",
     )
-    variant("python", default=False, description="Build Python bindings")
+    variant("python", default=True, description="Build Python bindings")
     variant("doc", default=False, description="Build documentation")
     # Build type and debug symbols:
     # - Both Debug and Release builds have debug symbols enabled by default in
@@ -156,6 +162,15 @@ class Spectre(CMakePackage):
         default="system",
         description="Which memory allocator to use",
     )
+    variant(
+        "openmp",
+        default=False,
+        when="@2024.03.19:",
+        description=(
+            "Enable OpenMP parallelization in some parts of the code"
+            " (Python bindings and exporter)"
+        ),
+    )
     variant(
         "formaline",
         default=True,
@@ -169,15 +184,20 @@ class Spectre(CMakePackage):
     )
 
     # Compiler support
+    conflicts("%gcc@:8", when="@2022.06.14:")
     conflicts("%gcc@:6")
+    conflicts("%clang@:12", when="@2023.10.11:")
     conflicts("%clang@:7")
+    conflicts("%apple-clang@:12", when="@2023.10.11:")
     conflicts("%apple-clang@:10")
 
     # Build dependencies
+    depends_on("cmake@3.18:", when="@2023.02.09:", type="build")
     depends_on("cmake@3.12:", type="build")
     depends_on("python@2.7:", type="build")
 
     # Link dependencies
+    depends_on("charmpp@7.0.0:", when="@2022.09.02:")
     depends_on("charmpp@6.10.2:")
     depends_on("blaze@3.8")
     depends_on("boost@1.60:+math+program_options")
@@ -186,13 +206,14 @@ class Spectre(CMakePackage):
     depends_on("hdf5")
     depends_on("jemalloc", when="memory_allocator=jemalloc")
     depends_on("libsharp~mpi~openmp")
-    depends_on("libxsmm@1.16.1:")
+    depends_on("libxsmm@1.16.1:1")
     depends_on("blas")
     depends_on("lapack")
     depends_on("yaml-cpp@0.6:")
 
     # Test dependencies
-    depends_on("catch2@2.8:", type="test")
+    depends_on("catch2@3.4.0:3", when="@2023.08.18:", type="test")
+    depends_on("catch2@2.8:2", when="@:2023.07.29", type="test")
     depends_on("py-numpy@1.10:", type="test")
     depends_on("py-scipy", type="test")
     depends_on("py-h5py", type="test")
@@ -200,12 +221,19 @@ class Spectre(CMakePackage):
     # Python bindings
     with when("+python"):
         extends("python")
+        depends_on("python@3.8:", when="@2023.08.18:", type=("build", "run"))
         depends_on("python@3.7:", type=("build", "run"))
         depends_on("py-pybind11@2.6:", type="build")
+        depends_on("py-click", when="@2022.12.16:", type=("build", "run"))
+        depends_on("py-h5py@3.5.0:", type=("build", "run"))
+        depends_on("py-humanize", when="@2023.04.07:", type=("build", "run"))
+        depends_on("py-jinja2", when="@2023.07.29:", type=("build", "run"))
         depends_on("py-numpy@1.10:", type=("build", "run"))
         depends_on("py-scipy", type=("build", "run"))
         depends_on("py-matplotlib", type=("build", "run"))
-        depends_on("py-h5py", type=("build", "run"))
+        depends_on("py-pandas@1.5:1", when="@2023.04.07:", type=("build", "run"))
+        depends_on("py-pyyaml", type=("build", "run"))
+        depends_on("py-rich", when="@2022.12.16:", type=("build", "run"))
 
     # Docs
     with when("+doc"):
@@ -319,6 +347,7 @@ def cmake_args(self):
             self.define("USE_GIT_HOOKS", False),
             self.define("USE_IWYU", False),
             self.define_from_variant("USE_FORMALINE", "formaline"),
+            self.define_from_variant("ENABLE_OPENMP", "openmp"),
             self.define_from_variant("MEMORY_ALLOCATOR").upper(),
             self.define_from_variant("ENABLE_PROFILING", "profiling"),
             self.define("USE_PCH", True),