Accelerators have become a corner stone of parallel computing, ranging from scientific computing to artificial intelligence. At the application level, accelerators are controlled by submitting work into a stream, from which the work is executed by the hardware. Vendor-specific communication libraries such as NCCL and RCCL have integrated support for submitting communication operations onto a stream to enable ordering of communication and work on streams. It is safe to assume that stream-based computing will remain relevant for the foreseeable future. MPI has yet to catch up to this reality and prior proposals involved extensions of MPI that would incur significant additions to the API. In this work, we explore alternatives that involve only minor additions to the standard to enable the integration of MPI operations with compute stream. Our additions include i) associating streams with communication objects, ii) blocking streams until completion, and iii) synchronizing streams while progressing MPI operations. Our API is agnostic of the type of stream, reuses existing communication procedures and semantics, and enables integration with graph capturing. We provide a proof-of-concept implementation and show that stream integration of MPI operations can be beneficial.