If I have a 240v 20a circuit serving a single 240v 20a receptacle (12/3) can I leave the 240v receptacle in service then branch two 120v 20a circuits from it?
Perhaps. Firstly, without a time machine you have a 240V 20A receptacle and want to add 120V 20A receptacles.
You may need to replace the breaker with a dual-pole GFCI breaker as it's quite likely that the 120V circuits will need GFCI protection depending where they are and what version of code is adopted in your area at the time you do the work.
Other than that, yes, this is fine.