Technically, you can only sister the new joists if you face-nail them via the outside of the ribbon board as well as to the 2x6s. BUT, I'd consider this unsafe because the nails may work themselves loose from the ribbon board.
What you can do is leave enough room between them based on the room necessary to use joist hangers. In this manner, the 2x6s and the 2x12s are not touching each other but close enough to lend support to each other. I'm not sure how you're gonna handle the ends because they will carry a LOT of weight. If the ends are NOT doubled-up with 2x6s now, then perhaps that would be in order. From there, go 16" OC from the outside ribbon board. It may be prudent to speak to a carpenter/framer (or wait for someone else to help further on the BBS).