Any examples?
Do you make them fight left handed by going to the side where the right handed guy can only punch with the "weak" hand?
If the switch to match your stance.... switch yours stance and time them.
If they don't switch to match you.....
Attack the lead leg. If you hit them with good hard leg kicks, they may switch to protect the leg that is now sore. Or, use foot sweeps on the lead leg... if you start sweeping them, or at least getting close enough that you interrupt what they are doing and frustrate them, they may switch to try to force you to use an unfamiliar angle on your sweep.
Take away their jab and circle behind them, away from their power hand. The idea is to keep them turning the same way, until they get frustrated enough to switch.
Whether you are attacking the lead leg or the lead hand, always follow with a shot.... If you sweep, you should be going for the sweep.... if they lift their foot away, they are on one foot and unable to use power.... they are open for an immediate punch, you want your punch to land before their foot.... even if they block, you should be knocking them off-balance as they are on one foot. If the root the foot you are sweeping, again they just immobilized themselves... throw a punch that lands before they can reset their weight. (if you are allowed... if they defend a foot sweep, they are open for a hip throw...) If you are attacking their lead hand, as soon as you move over, throw your attack before he can turn towards you. It's like you are trying to get past that lead hand, so you can take his back.... you won't get to his back most of the time, but you will create an angle where you are facing him and he is facing where you used to be. From here everything should be open for you.
The most important point is that you decide which way you are going to fight. Do not let the other guy dictate that. Learn the adjustments you need to fight a rightie and a leftie. If you know how to exploit each side.... you will know what they are wanting to do to you.