Can there be more than one path for which Fermat's least time principle is obeyed?
Yes, there are situations in which more than one optical path can obey to Fermat's Least Time Principle. For example, you can imagine a reflecting ellipsoid in which you have a single, homogeneous medium. By geometrical construction, every path starting from a focus, going straight to mirror, being reflected and going back to the other focus has the same geometrical length and, since the medium is always the same, also the optical path is the same. Therefore, every optical path of this type will obey to Fermat's Least Time Principle.