Early game: Focus on making Vayne irrelevant. Jungler should gank bot whenever it's available and mid when not. Ganking for kills mid will mean your mid laner can also get a lead to roam bot and take down Vayne some more.
Mid game: Keep Vayne irrelevant. Most Vayne games go the same way: team groups 5 to push mid, Vayne stays bot and farms until she has caught up and is relevant. This is a mistake. If you have an irrelevant Vayne on the enemy team, keep her that way. Keep whoever can 1v1 her in the same lane and have them continue to make her irrelevant. If it's someone with TP, even better. Prioritize objectives whenever you get kills - you preferably want to win this one in the mid game as the enemy team scales pretty well.
Teamfights: Don't group up on eachother. A 4 or 5 man malphite ult in to yasuo ult, in to braum ult, is going to be a near certain ace. Have a well defined front and back line, so Malphite can only really ult 2 people in the front line and can't get close enough to ult the back line. One weakness of this comp is that Malphite, Yasuo, and Braum are all teamfight champions while Elise and Vayne are much better at making picks and splitting respectively. So if Vayne wants to farm up you send a person to stop her and that's 1 less person for Malphite to ult.
Late game: Done properly Vayne shouldn't be doing anywhere near as much damage as your ADC due to being far behind. If Elise isn't ahead you'll do really well prioritizing armor and health. If elise is ahead you should prioritize health with a mix of armor/mr. I'd still suggest a Banshee's Veil because it will often block Vayne's condemn and thus let you stick to her to kill her in the fights.
The alternatives of course would be:
- Pick counters in every lane and just win early
- Pick an even harder scaling team comp and draw out the game
- Pick a comp that can 1-3-1 very effectively
- Pick a godlike teamfight comp.