Multi-Engine Before Commercial?

My original plan was to finish the instrument rating and then do some
additional aerobatic training and a tailwheel endorsement before
starting the commercial. But for some reason, as I approach the end of
the instrument training, I've had an interest in doing the multi. I
know that I wouldn't be able to rent due to insurance, nor do I know
if I'd really want to given the small number of hours I'd have by the
time I completed it. It would be one more opportunity to increase my
knowledge and skills. And maybe I'd get asked to ride along with a few
pilots I know that are rated.

But does it make sense to do the multi before the Comm, and would I
receive more benefit from following my original plan?

Dave