A.M.A.A. - Ask Moonface Anything, Again

[Moonface]

Had to look up what mutt cats are and didn't realize they're just any non-pure breed cat and that's where the word moggie comes from; I always thought that word was just a really old slang term my granddad used for any cat.
Looking at a list of breeds, I'd love a cat that has the appearance of a Maine Coon or a Bengal. There were a few breeds I saw that look like they've been bred to the point of form over functionality similar to pugs, but I'm hoping the visual similarity is where it ends and those cat breeds don't have the horrific issues that pugs have.