Part of me thinks this happening wouldn't be due to a group/combatant/whatever entering the fray (the most likely candidate for this IMO being the World Government or the Navy, the former to protect their interests and status quo, the latter because Akainu decided to shift his priorities for whatever reason).
I think it'd be a bit more likely that the "3rd party" would actually be another battle or something going down-- like all the shit going down in the rest of the world (the Navy going after the Seven Warlords of the Sea, whatever went down in Alabasta, the Blackbeard Pirates on the move, the Revolutionaries' response to whatever happened at the Reverie, etc) spilling over into Wano from the outside (whether it be literally or by information trickling in and piquing interest). That might fuck shit up enough to segue into the worldwide war.
I'm also very much looking forward to the next intermission, we might get some spaces filled in after Act 3 gives us a hint to what the One Piece is.