The interesting word henotheism stands for "the worship of one God without denying the existence of other Gods", and is obviously distinct from polytheism ("belief in or worship of more than one God"), monotheism ("belief that there is but one God"), kathenotheism ("worship of several gods successively"), atheism ("belief that God does not exist") , agnosticism ("belief that nothing can be known concerning the existence of God"), theism ("belief in the existence of a God or Gods, specifically of a creator who intervenes in the universe"), deism ("belief in the existence of a supreme being, specifically of a creator who does not intervene in the universe") and pantheism ("belief that God can be identified with the universe, or worship that tolerates all Gods").

Whilst there are further distinctions, like hard polytheism (e.g. the ancient Hellenic Gods) and soft polytheism (e.g most forms of Hinduism), and inclusive monotheism (e.g. some Hindu creeds) and exclusive monotheism (e.g. Judaism, Christianity and Islam), I believe that there is a case for a new word extended in meaning from henotheism.

"The worship of many Gods without denying the existence of other Gods" - notice the substitution of "many" for "one", that distinguishes it from henotheism (and, of course, the clause following the "without", that separates it from polytheism).

This theology refers to a belief in a specific pantheon of Gods, whilst recognizing the existence of other pantheons and standalone Gods, but not worshipping them.

I believe this would fit most Hindu creeds (especially belief in contemporary urban India, where unprecedented cultural exchanges have taken place within the last half century), and hence will not denote a small minority of humanity.

What shall this new word be? It probably should have a "theism" towards the end, but the beginning (and the middle?) require some further thought. Here we need the etymological services of a classical philologist - perhaps someone familiar with ancient Greek (and Latin, Hebrew and Sanskrit?). I only have the barest acquaintance with these tongues, but will venture to suggest a candidate or two:

metahenotheism?
suprahenotheism?
polytolerartheism?

My friend EW suggests:

multitheism
kaleidotheism

What think you?

Sincerely,
SM