is it possible to isomerize alpha methyl styrene to beta methyl styrene???
I don't think so. I don't see how you can transfer the methyl group from the alpha to the beta position in a simple way. Maybe by using some sort of exotic rearrangement, but certainly not by something I am aware of.
Alpha methylstyrene is too stable as is. Not to mention for a rearrangement like that you would have to create a cation on a primary carbon vs a benzylic carbon. Isn't going to happen (obviously, there's always exceptions, but I don't think this is one)