Developing multiphysics applications that run on the supercomputers of the exascale era is a daunting task. The varying workload in different regions of a problem can make load balancing difficult, especially when simultaneously handling GPU and CPU resources. Task-based parallelism is a promising way out of this dilemma but it introduces significant complexity for the application developer and has not seen widespread adoption for that reason. I will introduce FleCSI, which is an open-source C++ framework developed at Los Alamos National Laboratory as part of the Advanced Simulation and Computing Program of the U.S. Department of Energy to mitigate these issues. It provides an abstraction layer aimed at multiphysics application developers to make it easy to use different task-based parallelism frameworks. This is achieved by expressing data access permissions in the types of the function arguments. FleCSI currently supports Legion and HPX, while also providing an MPI backend as a fallback. Data movement to and from host/device memory spaces as well as halo updates is handled transparently for the user. Performance portability is achieved through Kokkos. It is possible to run CPU and GPU tasks simultaneously and have the data moved as needed. FleCSI offers several base topologies, upon which developers can build so-called specializations for their specific data layout. Among these are N-dimensional arrays, unstructured meshes, tree, and set topologies. I will give some examples of the FleCSI programming model and show how we build the complex dependencies on various architectures through Spack. I will give an overview of several applications including the HARD code, an open-source radiation-hydrodynamics code on a structured mesh, and Moya, a low energy density ALE (Arbitrary Lagrangian Eulerian) code on an unstructured mesh. I will show benchmark results obtained on the AMD MI300A machines at Lawrence Livermore National Laboratory.