Polytheology: Syncretism, Process Theology, and "Polyamorotheism"
The insurmountable divide that people put between humans and gods in terms of our ability to understand them (e.g., "the Gods' ways are not our ways" -- a passage here paraphrased from the Hebrew Bible!), and of our abilities to communicate and negotiate with them, therefore, is not necessarily in operation. The gods may have a great deal more power, or knowledge, or freedom due to their position and their conditions of existence, but if they cannot be understood, communicated with, or related to, then the entire enterprise of religion and spirituality is useless entirely.
But, to use a human analogy, the individuality and volition of particular deities is not unlike the individuality and volition of particular humans. When a child is sent to school, the child does not learn from Teacher, the child learns from Mrs. Robertson or Mr. Danforth. We all laughed at the character of Karen on "Will & Grace" when she would refer to various service-people in her life as "Driver," "Pharmacist," and so forth, as if her wealth and privilege made her blind to individuality or the unique lives and personalities of the people she saw as her functional subordinates; they were only useful for their instrumental value in her life. But, how many of us do this in relation to our deities on a regular basis? If we are really to confront the problems -- as well as the potential wonders and beauties -- of polytheology, then this must be one of the initial issues to deal with: every deity is individual, particular, specific, and unique, just as each one of us is unique. One deity cannot simply stand in for another along functional lines, gender lines, or anything else.
However, the traditions within which I practice are syncretistic traditions, where things like Interpretatio Romana occurred in the past. This was a situation in which a deity from one culture was paired with that of another: Jupiter-Taranis, for example, or Zeus-Ammon. This type of syncretism occurs when two cultures come into contact with each other, and commonalities are sought between their diverse religious expressions. Polytheistic societies tend to be much better at doing this than are insistently and exclusively creedal monotheistic societies (and yet Christianity was quite good at syncretism at various points when it encountered non-Mediterranean cultures). But, given polytheistic cultures have also done it within their own cultures, it is not just an intercultural activity, it is intracultural.
Amun-Re and Re-Harakhte are both syncretized forms of the Egyptian solar deity Re, and yet the individual cults and these syncretized versions all continued to exist, no matter how much the popularity of some of them eclipsed others. The same is true of Greek culture: the Artemis of Sparta (Artemis Orthia), the Artemis of Athens (Artemis Brauron), and Artemis of Ephesus are not all the same deity initially, but whatever underlies all of them that defined "Artemis" to the wider Greek culture eventually was agreed upon, and in each of those locations, the particularities of the local tradition persisted even despite knowledge of the wider Artemisian context. The same is true of many other deities within many polytheistic cultures.
The syncretized forms of deities, however, often did become separate from their "source" deities. The Graeco-Egyptian deity Hermanubis was a combination of Hermes Psychopompos and Anubis, and yet in certain Roman Imperial period inscriptions, Hermanubis and Anubis are not taken as synonymous, but as separate deities. But, Hermanubis went on to have a "career" of his own. Another popular Hermes syncretism, Hermes Trismegistos ("Thrice-Great"), was a combination with the Egyptian god Djehuty/Thoth, who had a wide-ranging importance in later Hermetic tradition, Renaissance magic, and general esoteric and occult practice. The various deities who contributed to the imagery and iconography of Serapis all continued after his introduction, but Serapis himself went on to have a truly international career across the late Roman Empire. The same is true of Zeus-Ammon, the "pantheistic" version of Isis, and a variety of others.