Has a starting quarterback ever played in the Super Bowl for two or more different teams?

Kurt Warner won Super Bowl XXXIV but lost Super Bowl XXXVI with the St. Louis Rams, then lost Super Bowl XLIIII with the Arizona Cardinals.

Craig Morton also was the starting Quarterback to lose the Super Bowl for a NFC team Dallas Cowboys in SB V and an AFC team Denver Broncos SB XII.

Kurt Warner Super Bowl appearances :

Super Bowl 34 (January 30, 2000) St. Louis Rams 23-16 Tennessee Titans

Super Bowl 36 (February 3, 2002) New England Patriots 20-17 St. Louis Rams

Super Bowl 43 (February 1, 2009) Pittsburgh Steelers 27-23 Arizona Cardinals