Transfering sculpt to new base mesh?

I have made a sculpt of a head using a base mesh and used multi-resolution. Im quite far on in the sculpt and the likeness is looking good. The only thing is, I wish I had used a different base mesh to begin with… Does anyone know a way of transfering what I have already sculpted onto a different base mesh? I dont have a clue myself but if there is a genius who knows how this can be done (if it can) I would as happy as a pig in mud…

Cheers