I'm considering something like that too but not too crazy. I'm experimenting on an RTW trip but all within 24-36 hours of one another as a celebration of my finishing college and admission to university. Here's the itin:
SIN-LHR (SQ), LHR-FRA (LH), FRA-JFK (SQ), JFK-SFO (UA/CO), SFO-SEA (UA/VX) all in F and within 24 hours in between.
So have fun if you're going to do so!