I'm also on an L1B visa, to my knowledge there's no such flexibility, to the point that you'd have to move back to your country or have a new company file a brand new H1B application if you wanted to move, I don't know how frequently this is done.
An L1B visa is actually very restrictive as I understand it, any insight Peter had would certainly be interesting.
Thanks for your replies guys, how likely is it to get sponsored by another company taking into account you already have experience in the US and currently live in the US? Also, is it possible for me to set up a startup if I wanted to? Thanks!!