Composability is one of seven reasons for the long-standing and continuing success of MPI. Extending MPI by composing its operations with user-level operations provides useful integration with the progress engine and completion notification methods of MPI. However, the existing extensibility mechanism in MPI (generalized requests) is not widely utilized and has significant drawbacks. MPI can be generalized via scheduled communication primitives, for example, by utilizing implementation techniques from existing MPI-3 nonblocking collectives and from forthcoming MPI-4 persistent and partitioned APIs. Non-trivial schedules are used internally in some MPI libraries; but, they are not accessible to end-users. Message-based communication patterns can be built as libraries on top of MPI. Such libraries can have comparable implementation maturity and potentially higher performance than MPI library code, but do not require intimate knowledge of the MPI implementation. Libraries can provide performance-portable interfaces that cross MPI implementation boundaries. The ability to compose additional user-defined operations using the same progress engine benefits all kinds of general purpose HPC libraries. We propose a definition for MPI schedules: a user-level programming model suitable for creating persistent collective communication composed with new application-specific sequences of user-defined operations managed by MPI and fully integrated with MPI progress and completion notification. The API proposed offers a path to standardization for extensible communication schedules involving user-defined operations. Our approach has the potential to introduce event-driven programming into MPI (beyond the tools interface), although connecting schedules with events comprises future work. Early performance results described here are promising and indicate strong overlap potential.