Talk to other players OOC. My favorite way to help characters play off each other is to create a character history with another player(s) and have that be incorporated IC. Rather than a bunch of complete strangers coming together for the first time, for some characters it could be a reunion, or they start off already being friends/rivals/ etc. with a pre-existing relationship. 

If you do start with all-strangers then talk to players OOC about how they’d like to see character relationships develop as the RP progresses. Communication, especially from the GM, is key when it comes to setting expectations and making sure everyone is included. I feel like a level of planning when it comes to character development among the players OOC also encourages more OOC discussion about the RP. And don’t forget to switch it up and do some scheming with other players/characters so you don’t catch yourself running off on unrelated side-quests with your new best bud. 

Those were always the sorts of RPs I’ve had the most fun with anyway.