It's governed by the fare rules. If you can access those you can see what the carrier allows. I forget what sites allow viewing (Zuji, maybe), but the stickies at the top of forums like Mileage Run or MilesBuzz usually have the latest info about what online tools have the best information.

U.S.-based carriers tend to be pretty strict on stopovers, counting anything over 4 hours domestically or 24 hours on an international itin as a stopover and then saying (especially for lowest fares) that you can't have any. Sometimes they might lighten up, like UA's $50 DEN stopover they had for a time, or making a connecting city an allowable stopover. Non-U.S. carriers are sometimes more flexible.