diff --git a/tools/toolchain/scripts/stage0/install_cmake.sh b/tools/toolchain/scripts/stage0/install_cmake.sh
index 8ec308be9c..5de1230bc7 100755
--- a/tools/toolchain/scripts/stage0/install_cmake.sh
+++ b/tools/toolchain/scripts/stage0/install_cmake.sh
@@ -20,23 +20,21 @@ cd "${BUILDDIR}"
 case "${with_cmake}" in
   __INSTALL__)
     echo "==================== Installing CMake ===================="
-    cmake_ver="3.31.7"
-    cmake_ext="sh"
+    cmake_ver="4.2.3"
     if [ "${OPENBLAS_ARCH}" = "arm64" ]; then
       if [ "$(uname -s)" = "Darwin" ]; then
         cmake_arch="macos-universal"
-        cmake_sha256="1cb11aa2edae8551bb0f22807c6f5246bd0eb60ae9fa1474781eb4095d299aca"
-        cmake_ext="tar.gz"
+        cmake_sha256="c2302d3e9c48daabee5ea7c4db4b2b93b989bcc89dae8b760880e00120641b5b"
       elif [ "$(uname -s)" = "Linux" ]; then
         cmake_arch="linux-aarch64"
-        cmake_sha256="ce8e32b2c1c497dd7f619124c043ac5c28a88677e390c58748dd62fe460c62a2"
+        cmake_sha256="e529c75f18f27ba27c52b329efe7b1f98dc32ccc0c6d193c7ab343f888962672"
       else
         report_error ${LINENO} \
           "cmake installation for ARCH=${OPENBLAS_ARCH} under $(uname -s) is not supported. You can try to use the system installation using the flag --with-cmake=system instead."
       fi
     elif [ "${OPENBLAS_ARCH}" = "x86_64" ]; then
       cmake_arch="linux-x86_64"
-      cmake_sha256="b7a5c909cdafc36042c8c9bd5765e92ff1f2528cf01720aa6dc4df294ec7e1a0"
+      cmake_sha256="5bb505d5e0cca0480a330f7f27ccf52c2b8b5214c5bba97df08899f5ef650c23"
     else
       report_error ${LINENO} \
         "cmake installation for ARCH=${OPENBLAS_ARCH} under $(uname -s) is not supported. You can try to use the system installation using the flag --with-cmake=system instead."
@@ -47,14 +45,15 @@ case "${with_cmake}" in
     if verify_checksums "${install_lock_file}"; then
       echo "cmake-${cmake_ver} is already installed, skipping it."
     else
-      retrieve_package "${cmake_sha256}" "cmake-${cmake_ver}-${cmake_arch}.${cmake_ext}"
+      retrieve_package "${cmake_sha256}" "cmake-${cmake_ver}-${cmake_arch}.tar.gz"
       echo "Installing from scratch into ${pkg_install_dir}"
       mkdir -p ${pkg_install_dir}
       if [ "${cmake_arch}" = "macos-universal" ]; then
-        tar --strip-components=3 -xvf cmake-${cmake_ver}-${cmake_arch}.${cmake_ext} -C ${pkg_install_dir} > install.log 2>&1 || tail_excerpt install.log
+        strip_components=3
       else
-        /bin/sh cmake-${cmake_ver}-${cmake_arch}.${cmake_ext} --prefix=${pkg_install_dir} --skip-license > install.log 2>&1 || tail_excerpt install.log
+        strip_components=1
       fi
+      tar --strip-components=${strip_components} -xvf cmake-${cmake_ver}-${cmake_arch}.tar.gz -C ${pkg_install_dir} > install.log 2>&1 || tail_excerpt install.log
       write_checksums "${install_lock_file}" "${SCRIPT_DIR}/stage0/$(basename ${SCRIPT_NAME})"
     fi
     ;;
diff --git a/tools/toolchain/scripts/stage3/install_libxc.sh b/tools/toolchain/scripts/stage3/install_libxc.sh
index 989c717e1e..480aef13a5 100755
--- a/tools/toolchain/scripts/stage3/install_libxc.sh
+++ b/tools/toolchain/scripts/stage3/install_libxc.sh
@@ -53,6 +53,7 @@ case "$with_libxc" in
       fi
 
       # CP2K does not make use of fourth derivatives, so skip their compilation with -DDISABLE_KXC=OFF
+      # Add "-DCMAKE_POLICY_VERSION_MINIMUM=3.5" to keep legacy compatibility for CMake version 4.x
       CFLAGS="${LIBXC_CFLAGS}" cmake \
         -DCMAKE_INSTALL_PREFIX="${pkg_install_dir}" \
         -DCMAKE_INSTALL_LIBDIR=lib \
@@ -60,6 +61,7 @@ case "$with_libxc" in
         -DBUILD_TESTING=OFF \
         -DENABLE_FORTRAN=ON \
         -DDISABLE_KXC=OFF \
+        -DCMAKE_POLICY_VERSION_MINIMUM=3.5 \
         .. > configure.log 2>&1 || tail_excerpt configure.log
       make -j $(get_nprocs) > make.log 2>&1 || tail_excerpt make.log
       make install > install.log 2>&1 || tail_excerpt install.log
diff --git a/tools/toolchain/scripts/stage4/install_cosma.sh b/tools/toolchain/scripts/stage4/install_cosma.sh
index 0828efc820..ea94e7212d 100755
--- a/tools/toolchain/scripts/stage4/install_cosma.sh
+++ b/tools/toolchain/scripts/stage4/install_cosma.sh
@@ -142,7 +142,15 @@ case "$with_cosma" in
       fi
       cd ..
 
-      cd COSMA-${cosma_ver} && mkdir build-cpu && cd build-cpu
+      cd COSMA-${cosma_ver}
+      # Fix two bugs in src/cosma/CMakeLists.txt:
+      # 1) COSMA_GPU_VENDOR is undefined, should be COSMA_GPU_BACKEND; remove quotes around OFF
+      # 2) IN_LIST generator expression: quotes break list parsing, and BLISi is a typo for BLIS
+      sed -i 's|\$<\$<STREQUAL:\${COSMA_GPU_VENDOR},"OFF">:cosma::BLAS::blas>|$<$<STREQUAL:${COSMA_GPU_BACKEND},OFF>:cosma::BLAS::blas>|' \
+        "src/cosma/CMakeLists.txt"
+      sed -i 's|\$<\$<NOT:\$<IN_LIST:\${COSMA_BLAS_VENDOR},"MKL;BLISi;OFF">>:COSMA_WITH_BLAS>|$<$<NOT:$<IN_LIST:${COSMA_BLAS_VENDOR},MKL;BLIS;OFF>>:COSMA_WITH_BLAS>|' \
+        "src/cosma/CMakeLists.txt"
+      mkdir build-cpu && cd build-cpu
       cmake \
         -DCMAKE_INSTALL_PREFIX="${pkg_install_dir}" \
         -DCMAKE_INSTALL_LIBDIR=lib \
diff --git a/tools/toolchain/scripts/stage4/install_scalapack.sh b/tools/toolchain/scripts/stage4/install_scalapack.sh
index a50de29454..b717e2cdf1 100755
--- a/tools/toolchain/scripts/stage4/install_scalapack.sh
+++ b/tools/toolchain/scripts/stage4/install_scalapack.sh
@@ -35,6 +35,9 @@ case "$with_scalapack" in
       [ -d scalapack-${scalapack_ver} ] && rm -rf scalapack-${scalapack_ver}
       tar -xzf ${scalapack_pkg}
 
+      # Change the CMake policy requirement to keep legacy compatibility for CMake version 4.x
+      sed -e 's/2.8/3.5/g' -i scalapack-${scalapack_ver}/BLACS/INSTALL/CMakeLists.txt
+
       mkdir -p "scalapack-${scalapack_ver}/build"
       pushd "scalapack-${scalapack_ver}/build" > /dev/null
 
diff --git a/tools/toolchain/scripts/stage8/install_trexio.sh b/tools/toolchain/scripts/stage8/install_trexio.sh
index 591a0853c5..b8cd1dc1f1 100755
--- a/tools/toolchain/scripts/stage8/install_trexio.sh
+++ b/tools/toolchain/scripts/stage8/install_trexio.sh
@@ -6,8 +6,8 @@
 [ "${BASH_SOURCE[0]}" ] && SCRIPT_NAME="${BASH_SOURCE[0]}" || SCRIPT_NAME=$0
 SCRIPT_DIR="$(cd "$(dirname "$SCRIPT_NAME")/.." && pwd -P)"
 
-trexio_ver="2.6.0"
-trexio_sha256="02b692c7792b4c8d041b1eeacdf144dca333a6ea699f66e911489768586de335"
+trexio_ver="2.6.1"
+trexio_sha256="c3694ec1528632a386a2af89199c75d70ecd45bfcc2ca1d4ccccbfa1308ad5fa"
 
 source "${SCRIPT_DIR}"/common_vars.sh
 source "${SCRIPT_DIR}"/tool_kit.sh
@@ -40,8 +40,17 @@ case "$with_trexio" in
       tar -xzf trexio-${trexio_ver}.tar.gz
       cd trexio-${trexio_ver}
 
-      ./configure --prefix="${pkg_install_dir}" --libdir="${pkg_install_dir}/lib" > configure.log 2>&1 || tail_excerpt configure.log
+      CMAKE_OPTIONS="-DCMAKE_VERBOSE_MAKEFILE=ON"
+      if [ "${MPI_MODE}" != "no" ]; then
+        CMAKE_OPTIONS="-DCMAKE_C_COMPILER=${MPICC}"
+      fi
 
+      mkdir build && cd build
+      cmake \
+        -DCMAKE_INSTALL_PREFIX="${pkg_install_dir}" \
+        -DCMAKE_INSTALL_LIBDOR="lib" \
+        ${CMAKE_OPTIONS} \
+        .. > configure.log 2>&1 || tail_excerpt configure.log
       make -j $(get_nprocs) >> make.log 2>&1 || tail_excerpt make.log
       make install > install.log 2>&1 || tail_excerpt install.log
       cd ..