If I have separate players for each flow, is it possible to have a separate mixer window for each flow?
No, there is only a single Mixer window for a given project (and indeed really only one can be operable for the application as a whole, since you cannot have more than one project able to play back at the same time).
Perhaps some extension of the automation capability would accomplish what Bengt is talking about.
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On edit, actually, can’t you ALREADY effectively achieve a different mix in each flow using the existing automation capabilities?