if I move a multi energy to a pokemon that already has a special energy, would it change to colorless or am I not allowed to do that?
And lets say it tells me I can only move lightning energy
If the Multi is providing all colors at the time you try to move it, it will move.
Once it is attached to the new Pokemon, and that Pokemon has a Special Energy attached to it, now Multi, per the text on it, won't provide any more colors of energy.