Actually… Kyubey is successfully staving off the heat-death of the universe (implied to also be the ultimate — and so far unsuccessful — goal of Entities), using the power of Emotion: most especially grief.
So, you could probably manage a decent PMMM crossover where Kyubey decides to take people's Shards instead of their Souls, with the end-goal of turning Zion into an immensely powerful Grief Seed. It would let you underline that Kyubey is not actually "evil" in the traditional sense, rather that Incubators have a completely alien sense of ethics/morality and emotion that don't align with human norms (partly due to being a hive-mind species, so they see individuals as being expendable, in the same way that you accept that a lightbulb might burn-out). Incubators are heavily goal-driven, so discovering a new, better source of power than pubescent/prepubescent human girls would be a valid reason to change modus operandi — and Lesser Shards might even voluntarily sacrifice themselves if it combats entropy for the species/entity, due to their own varying levels of individuality.
You'd be left with Parahumans vs Magical Girls (well… I guess the 'Girls' part would no longer be mandatory if it was the Shard that was important), with Cauldron stuck somewhere in the middle trying to decide which side to support for the best chance of safely taking down Zion and saving humanity. (Because, if they back the Magical Girls, and then the Incubators decide to resume 'harvesting' humanity…)