Well, support Pokemon in doubles prefer to the stats of their opponents.
Why? Because there is almost no switching in doubles, and pressuring the opponent to switch can lead to a predicted KO. Pokemon in doubles usually prefer to stay in until they faint, but if they're an attacker and their stats are lowered, you will either have to switch or deal with doing lesser damage.
Raising your own stats in doubles is fine, but it's more effective (in my opinion) to just lower the opponents attacking stats so you can stay in the battle longer.
The most notable stat lowering Pokemon, from what I've seen, is Incineroar. With Intimidate, Snarl, and Parting Shot, it can keep switching out and lowering offensive stats. This gives its teammates "fake" bulk, even though they might not actually be bulky, with the opponents Attack and Special Attack lowered, it seems like they are.
Hope this helps! :)