The BMP grow via marriage alliances
With linlin presumably dead, the BMP need a new yonko to fall under, otherwise they will get destroyed by the admirals or other yonko.
Teach might be a bastard, but Kata would rather suck it up and join their crew than risk the lives of his family trying to make it by themselves.
Hence I think one of the BBP will end up marrying Pudding, allying the BM remnants with Teach. Sanji will then save Pudding from her marriage by defeating the guy who married her.
With linlin presumably dead, the BMP need a new yonko to fall under, otherwise they will get destroyed by the admirals or other yonko.
Teach might be a bastard, but Kata would rather suck it up and join their crew than risk the lives of his family trying to make it by themselves.
Hence I think one of the BBP will end up marrying Pudding, allying the BM remnants with Teach. Sanji will then save Pudding from her marriage by defeating the guy who married her.