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If I remember the implementation of "peek" right, it may do what you want. But the documentation doesn’t guarantee much about its behaviour; see Issue 5811.
Anyway, I agree that a "getbuffn" method (or property) would be nice. (Perhaps with a better name!) But please don’t add it to the abstract APIs like BufferedIOBase. It could break compatibility with third-party implementations, or make the API complicated with little benefit. Just extend the concrete APIs like BufferedReader.
Two other use cases where the "peek" implementation won’t help, but "getbuffn" would:
1. Issue 32561: Decide whether a non-blocking "read" call is possible, or if a background read (e.g. of a regular "disk" file) should be started instead.
2. Get the pending unread data before it is lost by calling "BufferedReader.detach".