In the US, any person may operate under the direct supervision of an operator of a higher class. This is how the GOTA (get-on-the-air) stations work at field day, but it's applicable at any time.
In most cases when operating in foreign countries under e.g. CEPT you do not gain any additional bands, but in some cases you may gain some additional operating ability because either the country authorizes specific extra bands through something other than CEPT or because their band does not exactly overlap with ours.
Any licensee (any service) may use any means necessary if normal channels are down if necessary for the protection of life or property against imminent danger. This is not quite what you asked because it does not grant them the privileges of a higher license class, rather "any means necessary".
Recent graduates from one license class to another receive temporary operating privileges, signing CALLSIGN/AG or CALLSIGN/AE for new general or extra privileges as needed, until their upgrade is officially noted on the FCC ULS.
Many countries allow case-by-case exceptions for experimental purposes, such as permission to operate on an additional band for people experimenting with LF and MF communications.
Some countries allow operators to use a repeater controlled by a higher-class licensee to access extra bands, for example if a general class licensee has a repeater input on 2 meters or 440 and output on 10 meters, a technician using that repeater may have his signal repeated into a band that he could not transmit on directly.