Asynchronous task multiplexing and chaining

The described technology is directed towards sharing asynchronous (async) tasks between task chains, including in a way that prevents cancellation of lower-level chain entity from cancelling a shared async task. A shared async task is wrapped in multiplexer code that maintains lower-level entity identities as a set of listeners of the shared async task, and when a listener cancels, only removes that listener from the set of listeners so that the shared async task does not cancel as long as one listener remains in the set. Also described is optimization to share an async task, and wrapping tasks in cancel-checking code that prevents the task from running its work if the task is intended to be cancelled but is queued to run before the cancel request is queued to run.