I don't think threesomes would satisfy the urge to cheat for some people. Part of the thrill and lure of cheating for habitual cheaters is the sneaking around, the forbidden fruit, and the chance to have sex wirth someone other than their spouse/ significant other.
Even if these are not reasons that your partner cheats, are you prepared to continually share your partner and your bed with another? Once you start it, do you really think your partner will be content to be one- on- one with you? Also, what if the other person is more atractive than you? Better in bed? Has a better body? What if your partner wants to include the other person more than you are comfortable with?
I just don't see threesomes as something that will help your problem; I see threesomes as something that will make it worse.