From: Anagram | #001
I think the closest he comes to affecting the main plot is when Hojo tries to breed him with Aeris for absolutely no reason
There was totally a reason. Aeris wasn't going to live long enough to finish all the tests he had planned, so he was going to breed her. You can later imply that this is because of the longevity of Red XIII's species.
Okay, so it's a dumb reason and Hojo is an idiot who doesn't understand that cross-species breeding doesn't typically work or that even if it did an human/dog hybrid probably wouldn't be suitable for whatever the hell he is trying to accomplish, but it is a reason.
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"One toot on this whistle will take you to a far away land."
-Toad, SMB3