send the tanks up first, hopefully you hvae some soldiers and have them cast tms before they go up. Sometimes if you all go up and just attack the one target that agroed the tank you can fight for a good bit without gettting 5 or 6 on you.
If you cant avoid getting agg from multiple aliens all at once, make sure you've got mezzers working at the aliens, healers doing their job, and tanks casting single taunts on the ones that wont mezz. If worse comes to worse you can all jump down the lift again and reorganise yourself. The most important thing when going up a lift is to remember to get OFF the lift when you go up, just like in missions
Thats all I can think of that might help you guys out