"Multiple different" or "different" or "multiple"

It's perfectly correct. While, based on Ngrams, multiple different is a construction which has seen a fairly recent increase in use, starting in roughly 1980, many different means essentially the same thing and has been around for many years. The word multiple itself has undergone a recent increase in use, as well, so my guess is that this naturally led to the occasional use of multiple different instead of many different.

Why do people use many different instead of just saying many? My guess is to emphasize the fact that these many contain a lot of variety. If a store said We have many dresses, it would still be correct even if they were all the same design, and if they just said We have different dresses, they might just have two.

I agree that multiple different sizes is redundant, and could be simplified to multiple sizes. But redundancy is very common in everyday language use, and not all uses of multiple different or many different are redundant.

Saying multiple as in "multiple different sizes" is redundant, but it is not wrong.

Basing on the data reported from the Corpus of Contemporary American English, I can say that "multiple different" is not so frequently used, and it is less used than "many different." (The scale is logarithmic because the difference between the number of sentences containing one phrase and the other.)

I then looked for sentences where “multiple different" and "many different" are followed by a noun, and I have obtained the following results.