This reminds me of "The Three Christs of Ypsilanti":

    Rokeach brought together three men who each claimed to be Jesus 
    Christ and confronted them with one another's conflicting claims, 
    while encouraging them to interact personally as a support group.
    [...]
    While initially the three patients quarreled over who was holier and 
    reached the point of physical altercation, they eventually each 
    explained away the other two as being patients with a mental 
    disability in a hospital, or dead and being operated by machines.

https://en.wikipedia.org/wiki/The_Three_Christs_of_Ypsilanti