Traditionally, boxing trainers have told their students not to switch stances against an uncooperative opponent. It's not a question of can you do it, but should you. After all, this isn't dancing or gymnastics; no boxing judge will ever downgrade you because you didn't maintain a style. But switching stances is a high-risk, high-reward move; it can throw off your opponent and make you highly vulnerable.
Fighters are constantly on the move, stepping forward, backward and side-to-side, but they never cross their feet. Crossing your feet puts you off balance, making you susceptible to your opponent's attacks and sapping power from your own punches. To switch stances, you need to cross your feet momentarily. Most boxers will launch a round of jabs to cover the move.
Most boxers are right-handed, which means they're used to competing against right-handed fighters. Switching from orthodox to southpaw stances can open your opponent up to more attacks, since they'll be coming in from different angles. Boxing great Marvin Hagler started his career as an orthodox fighter, but switched to southpaw to get his power right hand closer to his opponents' chin.
There's a reason most boxers and boxing trainers maintain one stance: it's difficult to do both. Fighting with your dominant hand in back gives you a powerful right cross and a sturdy defense against power punches. Switching stances puts your dominant hand in front, weakening your defensive abilities and taking some sting out of your rear-hand punch. If you're not comfortable fighting from both, you're more likely to make errors in footing and positioning.
Most boxers might refuse to switch stances, but there are always exceptions. Unorthodox right-handed boxer Roy Jones Jr. often switched stances to confuse opponents, while left-hander Oscar De La Hoya fought from an orthodox stance, similar to Hagler. Pound-for-pound great Manny Pacquiao traditionally fought out of a southpaw stance, but trained extensively in the orthodox stance to develop his left hand. Erik Morales switched from orthodox to southpaw in the last two rounds of a March 2005 meeting with Pacquiao. He won, but most pundits saw it as a foolish move designed to make the bout more exciting.