In Judo and BJJ contexts, the two on one grip break can be used to secure an overhook on the arm the opponent was grabbing you with.
To do this, initiate the two on one grip break. Then, holding on to the cross grip (if its the opponent’s right hand, you will hold with your right hand), let go with the non-crossed grip while pulling up and behind your head with the cross grip. Swim your head and non-overhooked under and then over the opponent’s arm. Once you secure a grip with the overhook on the opponent’s lapel, you can let go with your cross grip.
This can be done from standing or from different guards such as closed guard.