diff --git a/CMakeLists.txt b/CMakeLists.txt
new file mode 100644
index 0000000..0a07326
--- /dev/null
+++ b/CMakeLists.txt
@@ -0,0 +1,114 @@
+cmake_minimum_required(VERSION 3.24.0)
+
+project(cantera-dependency-superbuild)
+
+include(ExternalProject)
+
+set(DOWNLOAD_DIR "/cache")
+
+set(BOOST_VERSION 1.85.0)
+ExternalProject_Add(
+    boost
+    URL https://github.com/boostorg/boost/releases/download/boost-${BOOST_VERSION}/boost-${BOOST_VERSION}-cmake.tar.xz
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_BUILD_TYPE:STRING=release
+        -DBOOST_INCLUDE_LIBRARIES:STRING="algorithm;dll;stacktrace;core;math;numeric/ublas;serialization;multi_array"
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(LIBAEC_VERSION 1.0.6)
+set(LIBAEC_PATCHFILE)
+ExternalProject_Add(
+    libaec
+    URL https://gitlab.dkrz.de/k202009/libaec/uploads/45b10e42123edd26ab7b3ad92bcf7be2/libaec-${LIBAEC_VERSION}.tar.gz
+    PATCH_COMMAND patch -p0 < ${LIBAEC_PATCHFILE}
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_INSTALL_LIBDIR:STRING=lib
+        -DBUILD_TESTING:BOOL=OFF
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(LIBHDF5_VERSION 1.14.2)
+set(LIBHDF5_SHORT_VERSION 1.14)
+ExternalProject_Add(
+    libhdf5
+    URL https://www.hdfgroup.org/ftp/HDF5/releases/hdf5-${LIBHDF5_SHORT_VERSION}/hdf5-${LIBHDF5_VERSION}/src/hdf5-${LIBHDF5_VERSION}.tar.gz
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_INSTALL_PREFIX:STRING=/usr/local
+        -DHDF5_ENABLE_Z_LIB_SUPPORT:BOOL=ON
+        -DHDF5_ENABLE_SZIP_SUPPORT:BOOL=ON
+        -DHDF5_BUILD_EXAMPLES:BOOL=OFF
+        -DBUILD_TESTING:BOOL=OFF
+    DEPENDS libaec
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(EIGEN_VERSION 3.4.0)
+ExternalProject_Add(
+    eigen
+    URL https://gitlab.com/libeigen/eigen/-/archive/${EIGEN_VERSION}/eigen-${EIGEN_VERSION}.tar.bz2
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DEIGEN_BUILD_DOC:BOOL=OFF
+        -DBUILD_TESTING:BOOL=OFF
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(YAML_CPP_VERSION 0.8.0)
+ExternalProject_Add(
+    yamlcpp
+    URL https://github.com/jbeder/yaml-cpp/archive/refs/tags/${YAML_CPP_VERSION}.tar.gz
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_INSTALL_LIBDIR:STRING=lib
+        -DYAML_CPP_DISABLE_UNINSTALL:BOOL=OFF
+        -DYAML_CPP_FORMAT_SOURCE:BOOL=OFF
+        -DBUILD_TESTING:BOOL=OFF
+        -DBUILD_SHARED_LIBS:BOOL=OFF
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(SUNDIALS_VERSION 7.0.0)
+ExternalProject_Add(
+    sundials
+    URL https://github.com/LLNL/sundials/releases/download/v${SUNDIALS_VERSION}/sundials-${SUNDIALS_VERSION}.tar.gz
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_BUILD_TYPE:STRING=release
+        -DCMAKE_INSTALL_LIBDIR:STRING=lib
+        -DBUILD_SHARED_LIBS:BOOL=OFF
+        -DEXAMPLES_INSTALL:BOOL=OFF
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(FMT_VERSION 10.2.1)
+ExternalProject_Add(
+    fmt
+    URL https://github.com/fmtlib/fmt/releases/download/${FMT_VERSION}/fmt-${FMT_VERSION}.zip
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_INSTALL_LIBDIR:STRING=lib
+        -DFMT_DOC:BOOL=OFF
+        -DFMT_TEST:BOOL=OFF
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
+
+set(HIGHFIVE_VERSION 2.9.0)
+ExternalProject_Add(
+    highfive
+    URL https://github.com/BlueBrain/HighFive/archive/refs/tags/v${HIGHFIVE_VERSION}.tar.gz
+    CMAKE_GENERATOR Ninja
+    CMAKE_CACHE_ARGS
+        -DCMAKE_BUILD_TYPE:STRING=release
+        -DHIGHFIVE_UNIT_TESTS:BOOL=OFF
+        -DHIGHFIVE_USE_BOOST:BOOL=ON
+        -DHIGHFIVE_USE_EIGEN:BOOL=ON
+        -DHIGHFIVE_EXAMPLES:BOOL=OFF
+        -DHIGHFIVE_BUILD_DOCS:BOOL=OFF
+        -DBoost_NO_BOOST_CMAKE:BOOL=OFF
+    DEPENDS boost eigen libhdf5
+    DOWNLOAD_DIR ${DOWNLOAD_DIR}
+)
diff --git a/Dockerfile b/Dockerfile
index 252ba07..62ffc19 100644
--- a/Dockerfile
+++ b/Dockerfile
@@ -4,27 +4,21 @@
 ARG TARGET_ARCH
 FROM quay.io/pypa/manylinux_2_28_${TARGET_ARCH}:2024-07-15-c746fd8
 
-ARG BOOST_VERSION=1.85.0
-ARG HDF5_VERSION=1.14.2
 ARG NINJA_VERSION=1.12.1
 # Has to be repeated here so it's imported from the "top level" above the FROM
 ARG TARGET_ARCH
 
-ENV HDF5_VERSION=${HDF5_VERSION} \
-    HDF5_DIR=/usr/local \
-    BOOST_DIR=/usr/local \
-    BOOST_VERSION=${BOOST_VERSION}
+COPY CMakeLists.txt libaec_cmakelists.patch /tmp/
 
 RUN --mount=type=cache,target=/cache \
     if [[ "$TARGET_ARCH" == "aarch64" ]]; then NINJA_ARCH="-aarch64"; else NINJA_ARCH=""; fi \
     && echo "Getting Ninja for '${NINJA_ARCH}'" \
     && curl -fsSL -o /cache/ninja-linux.zip https://github.com/ninja-build/ninja/releases/download/v${NINJA_VERSION}/ninja-linux${NINJA_ARCH}.zip \
     && unzip /cache/ninja-linux.zip -d /usr/local/bin \
-    && ninja --version
-COPY install_libaec.sh libaec_cmakelists.patch install_hdf5.sh install_boost.sh /tmp/
-RUN --mount=type=cache,target=/cache \
-    bash /tmp/install_libaec.sh
-RUN --mount=type=cache,target=/cache \
-    bash /tmp/install_hdf5.sh
-RUN --mount=type=cache,target=/cache \
-    bash /tmp/install_boost.sh
+    && ninja --version \
+    && mkdir build \
+    && pushd build \
+    && cmake -G Ninja -DLIBAEC_PATCHFILE=/tmp/libaec_cmakelists.patch ../tmp \
+    && ninja \
+    && popd \
+    && rm -rf build
diff --git a/install_boost.sh b/install_boost.sh
deleted file mode 100644
index 003d60a..0000000
--- a/install_boost.sh
+++ /dev/null
@@ -1,19 +0,0 @@
-set -euo pipefail
-
-pushd /tmp
-
-BOOST_DOWNLOAD_FILE="/cache/boost-cmake.tar.xz"
-curl -fsSL -o $BOOST_DOWNLOAD_FILE https://github.com/boostorg/boost/releases/download/boost-${BOOST_VERSION}/boost-${BOOST_VERSION}-cmake.tar.xz
-tar -xf $BOOST_DOWNLOAD_FILE -C /tmp
-mkdir -p boost-${BOOST_VERSION}/build
-pushd boost-${BOOST_VERSION}/build
-
-cmake -G "Ninja" \
-    -DCMAKE_BUILD_TYPE=release \
-    -DBOOST_INCLUDE_LIBRARIES="algorithm;dll;stacktrace;core;math;numeric/ublas;serialization;multi_array" \
-    ..
-ninja install
-
-popd
-
-rm -rf boost-${BOOST_VERSION}
diff --git a/install_hdf5.sh b/install_hdf5.sh
deleted file mode 100644
index beb7ab0..0000000
--- a/install_hdf5.sh
+++ /dev/null
@@ -1,35 +0,0 @@
-set -euo pipefail
-
-echo "Installing zlib with yum"
-yum -y install zlib-devel
-
-pushd /tmp
-
-# This seems to be needed to find libsz.so.2
-ldconfig
-
-echo "Downloading & unpacking HDF5 ${HDF5_VERSION}"
-HDF5_DOWNLOAD_FILE="/cache/hdf5-${HDF5_VERSION}.tar.gz"
-#                                   Remove trailing .*, to get e.g. '1.12' ↓
-curl -fsSL -o $HDF5_DOWNLOAD_FILE "https://www.hdfgroup.org/ftp/HDF5/releases/hdf5-${HDF5_VERSION%.*}/hdf5-$HDF5_VERSION/src/hdf5-$HDF5_VERSION.tar.gz"
-tar -xzf $HDF5_DOWNLOAD_FILE -C /tmp
-mkdir -p hdf5-${HDF5_VERSION}/build
-pushd hdf5-$HDF5_VERSION/build
-
-echo "Configuring, building & installing HDF5 ${HDF5_VERSION} to ${HDF5_DIR}"
-cmake -G "Ninja" \
-    -DCMAKE_INSTALL_PREFIX=${HDF5_DIR} \
-    -DHDF5_BUILD_CPP_LIB=ON \
-    -DHDF5_ENABLE_Z_LIB_SUPPORT=ON \
-    -DHDF5_ENABLE_SZIP_SUPPORT=ON \
-    -DHDF5_BUILD_EXAMPLES=OFF \
-    -DBUILD_TESTING=OFF \
-    ..
-ninja install
-popd
-
-# Clean up to limit the size of the Docker image
-echo "Cleaning up unnecessary files"
-rm -r hdf5-$HDF5_VERSION
-
-yum -y erase zlib-devel
diff --git a/install_libaec.sh b/install_libaec.sh
deleted file mode 100644
index dc76127..0000000
--- a/install_libaec.sh
+++ /dev/null
@@ -1,27 +0,0 @@
-# libaec implements szip compression, so the optional szip filter can be built
-# in HDF5.
-set -euo pipefail
-
-pushd /tmp
-
-aec_version="1.0.6"
-
-echo "Downloading libaec"
-LIBAEC_DOWNLOAD_FILE="/cache/libaec-${aec_version}.tar.gz"
-# The URL includes a hash, so it needs to change if the version does
-curl -fsSL -o $LIBAEC_DOWNLOAD_FILE https://gitlab.dkrz.de/k202009/libaec/uploads/45b10e42123edd26ab7b3ad92bcf7be2/libaec-${aec_version}.tar.gz
-tar -zxf $LIBAEC_DOWNLOAD_FILE -C /tmp
-
-echo "Building & installing libaec"
-mkdir -p libaec-${aec_version}/build
-pushd libaec-$aec_version
-patch -p0 < /tmp/libaec_cmakelists.patch
-pushd build
-cmake -G "Ninja" -DCMAKE_INSTALL_PREFIX=/usr/local -DCMAKE_INSTALL_LIBDIR=lib -DBUILD_TESTING=OFF ..
-ninja install
-
-popd
-
-# Clean up the files from the build
-popd
-rm -r libaec-$aec_version