Exopsychology is a sub-discipline of psychology concerned with how humans contemplateextraterrestrials as well as forming hypothesis about how these beings may think, feel and behave. While researching the former is undoubtedly a subject for empirical science, aspects of the latter remain uncertain. Given the contemporary scientific insight, it may still be possible to identify a set of cornerstones and eventually create a space of possible configurations of the extraterrestrial mind. Here, we identify three basic compatibility requirements: first, any form of life must navigate internal and external (environmental) demands and thus actively ensure the compatibility of its current state with the same demands. Second, any advanced cognitive development and the emergence of remotely detectable technosignatures require not only the relevant capabilities for manipulation but also compatibility with a permissive environment. Lastly, requirements also concern the compatibility of extraterrestrial thinking and behaviour with our search method. In its most basic understanding, search for extraterrestrial intelligence (SETI) searches for something done by somebody. However, the meaning of this simple formula and the psychological theory behind it is underdeveloped. Hence, psychological aid is needed to assist SETI in its effort to reveal whether galactic information indicates the presence of a mere object or activity of an identified subject with whom humans may establish contact. The fact that people believe in and search for extraterrestrials emphasizes that psychology should pay attention to this domain of phenomena. Hence, different imaginations of the extraterrestrial, ranging from benign to cruel, from superior to equally developed, are briefly discussed regarding their emergence and function as coping and motivating mechanisms for the uncertain search.