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Am I being stupid here? I don't see how. My chain is long enough for 50/36 and the cage is (just barely) long enough to take up the slack for 34/11. If it can do both of those then the chain is (more than) long enough for 44/36 and the cage is more than long enough for 44/11. In the 44/36 the derailleur just takes up the slack. It would be like switching from 50/34 11-36 to 50/34 with a 21-30 cassette.
Perhaps it would result in suboptimal shifting it should work fine no?
Chain size is determined by the two largest sprockets.
Changing from 50t to 44t will definitely need two chains.