anything can happen! Usually, one of the feedback frequencies has a little more small signal gain, or is a little more close to 2Π degrees, so it builds up first and dominates the others by compressing the available gain. However, if something changes, like a slight change in temperature, etc, another frequency can take over.
Usually if you see multiple frequencies of oscillation, they are very far removed from each other, like tones at 200 KHz and other simultaneous tones at 400 MHz, etc.