How can I fix physics bounciness?

I have been designing some elevators for quite a while now, and it is working very well apart from the fact that if you have more than one player in it, it will bounce violently.

I tried welding the player to the platform, but that makes the player display the falling animation, and when the player moves the entire model moves with them.

Is there any other way to change the physics of a part/model so that it is not affected by the players standing on it?

Any help is greatly appreciated.