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The problems that this would solve are well-known pain points in the language, and they have been discussed many times over the years (e.g. Calling private methods from extensions in separate files) but so far no consensus has been reached that would allow a proposal to move forward.
To me, a big issue with a typeprivate like this is that the "owner" or originator of the type loses control of intended privacy within the type, due to the ability of other programmers to privately extend the type in other source code without limitation. In effect, therefore, typeprivate becomes something a lot like internal, which isn't really a solution.
I recommend that you search the forums for some discussions on this subject, to get a feeling for how little agreement there is. If you can find a meaningfully different approach (or at least meaningfully different answers to the existing objections!), I'm sure the community would love to hear about that. 