For the specific same-day change JFK-SFO-BUR => JFK-LAX / JFK-SFO-LAX: this is possible but unlikely if both of your flights are undersold and unaffected by mechanical, crew, weather, or other delays.

In the general case, hmm. Under other circumstances and pre-SHARES, I have had luck getting agents at SFO move me from SFO-BUR to SFO-LAX. A few times in the past, under the old UA computer system, I held SEA-SFO-BUR tickets and kindhearted agents at SFO helped me get onto an earlier SFO-LAX flight.

This was way back when United decided they didn't want SEA-LAX passengers traveling on mainline equipment and tightened routing rules accordingly. A couple of years ago, all published fares were valid on nonstop travel only (which meant United Express and CRJ-200s or CRJ-700s).

I grew weary of doing 954 miles on single-cabin equipment (or found it sold out) and sometimes booked the BUR trip instead. Sometimes the connection was so long that I had time at SFO to ask a mainline agent about loads on LAX flights before I trudged over to the regional jet gates. When connection times were long enough, and when SFO-LAX was heavily undersold and the agents weren't very busy, they were sometimes able to get me onto SFO-LAX instead of SFO-BUR.

This was totally outside of the fare rules! But the SFO sUA agents' occasional thoughtfulness and flexibility in confirming me a seat on an LAX flight when I didn't have a ticket to LAX was probably a good business decision. Heaven knows SEA-LAX is a high-yield shorthaul route (it often costs more than a transcon) and UA agents' flexibility helped keep me buying UA tickets even though it might have been a smarter short-term decision to book with AS or VX (!) instead.