Classical choice theory assumes that each person has a utility function, and chooses from each set of options an option that maximizes this utility. There are many empirical studies that refute this theory, showing that human choice cannot be explained by maxizing a utility function. Such results can be explained by assuming that each person has multiple utility functions, corresponding to different "frames". For example: a frame for each endowment, a frame for each status-quo, a frame for each time, etc.. The agent always maximizes one of these utility functions, depending on the active frame (see e.g. Bernhaim and Rangel and many others).
Apparently, every human choice can be explained by assuming an unbounded number of utility functions (e.g. a utility function for each moment in time), but a more meaningful explanation would involve a bounded number of utility functions.
My question is: from empirical evidence, is there some lower bound on the number of utility functions that humans hold simultaneously? For example: are there choice experiments that cannot be explained as maximizing one of two utility functions, but can be explained as maximizing one of three utility functions?