I dont think if there is a way to change sponsorship until and unless your current company agrees for it.

Now if you plan to exit and come back, then the RP process will depend on the company you are getting into. If its one of the Q company or well known MNC's it will finish in a month's time. I am telling you this because I did a recent change, left in December. New Co got me back in new visa, and we started the RP process in 2nd week of Jan, by Feb 1st week we all had our rp's