Splitting the triune god is a way.
We have one god who is Father, Son and Holy Spirit. They're all aspects or persons of the same god, they're all part of the same thing. Separate these things into actual, separated and subordinated deities, maybe add Mary as a fourth subordinate subject, and you have an henotheist Christianity. If it can still be called Christianity, but eh.
We can also make henotheist Judaism and Islam. Judaism WAS henotheist. What made it become purely monotheistic, I don't remember, presumably the return of some Jews from Babylon. Prevent this, and you have Jews who remained in Palestine still worshipping one god while recognizing the existance of others.
You could also have the Assyrians who settled in Palestine (those who would give birth to Samaritanism) undergo a similar process: they'd recognize the god of the Jews as the most important, putting in secondary importance but without fully renouncing to, the other pagan gods.
For Islam, there's talks of so-called Satanic Verses in the Quran. Satan would whisper to Muhammad that Allah has three daughters (the Meccan triad) but then he would purge these verses. Make sure Muhammad keeps these verses, and you have an henotheistic Islam. Islam. Kinda.