Error codes, check them:
http://www.cygnusx1.net/Supra/TechTi...ror_codes.aspx
Very few diagnostic errors actually result in the CEL remaining on.
TPS (Throttle Position Sensor) calibration:
http://www.cygnusx1.net/Supra/Librar...ction=FI&P=100
Does the vehicle have any aftermarket fuel management? Such as a piggyback system for adjusting the fuel (Apex'i SAFC, Apex'i Neo, MAFT Gen II, MAFT Pro)...
The BOV venting to atmosphere is probably the bulk of your problem, it's been covered here recently so do a search for all the details. Venting to the atmosphere on a system that isn't built/tuned for it causes the ECU to think there's still more air coming to the engine than there really is because the air it's already measured has just been tossed completely out of the system. For some people this simply causes the car to stumble everytime they shift and for others it flat out stalls.
If you've got the stock parts, try swapping the recirculating BOV (aka bypass valve or BPV) back on and see if the issues go away.
Check for error codes first though, there are other possible causes for this problem.