I suppose they'll try to cut it up but probably end up in New York

Corporations can make diversity jurisdiction more complicated. They are deemed to be "citizens" of the states where they are incorporated and where they maintain their headquarters. A California citizen would probably be successful in arguing for diversity jurisdiction in a lawsuit against a corporation incorporated in Delaware and headquartered in New York. If the corporation maintains significant business operations in California, diversity jurisdiction could be trickier.

Lawsuits with large numbers of parties increase the likelihood of a lack of diversity. In a class action against a large corporation, even one plaintiff from the same state as the defendant could derail an attempt to establish diversity jurisdiction, at least under the law before CAFA.