The MPccc scheme is indeed very natural and appealing, and the fact that it makes $2^{\aleph_0}$ very large without increasing the consistency strength of ZFC makes it an excellent answer to my question for CH. That's exactly the sort of things I was hoping for. Do you know (or have ideas about) analogous principles that could make $2^\kappa$ large for every $\kappa$ (in a vague sense) without increasing consistency strength?
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Comment by Gro-Tsen on Is there an “opposite” hypothesis to the (Generalized) Continuum Hypothesis?
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