Some feedback prevention approaches:
Changing the aim of the monitor speakers or the microphones. If the microphones are headsets (I assume they are for the musical), you can try to make sure the choreography doesn't take them (the singers and their microphones) too close to the near on-axis sound field of the speakers. You should always evaluate your speaker/microphone placement first
Another popular prevention approach is to adjust a parametric or graphic EQ in the signal path of the monitor speakers that cuts problem frequencies (the pitches of the feedback). Artful EQ can go a long way. See what you can do to make the feedback go away and still leave the sound easily discernable to the performers.
Also, if you're not already doing this, you should really be sending a different mix to the monitor speakers than goes to the house speakers. This way you can give the performers only what they need to hear to perform and possibly cut down on feedback by sending, say, a higher ratio of background music to performers, as the backing music is probably mostly what they need to stay on pitch, and you're probably not getting the feedback from those microphones, so they are "safer" feedback-wise.
There are some feedback-suppression devices on the market, but I don't have any personal experience with them. The theory behind them sounds promising, but I can't really speak to the quality of the execution.