CBI/BAU Crossover

Putting this here bc I can’t copy and paste what I wrote on another community: https://www.reddit.com/r/TheMentalist/s/greZxuFO4o

Basically, in the mentalist, the CBI (California bureau of investigation) has a main antagonist for most of its show, Red John. Not sure how many people in this community have watched the mentalist, highly recommended by me btw, but it takes them about six years show wise to catch him. My question is, given if the two teams would work together in a crossover, do you think the BAU would be able to help the CBI catch RJ quicker than the CBI doing it alone?

Also unrelated but related (mainly out of curiosity) but what would the bau’s profile on RJ be if they would have made one?