Golden rule overrides once per enhance phase?

" E: Place the top card of your deck in your momentum. Your opponent may play this ability. "

I play the enhance. Do to the second part, my opponent may now play it.

They do, so I can play it again right?

We could keep going back and forth until one of us declines to continue gaining momentum, or decks right?

Not that I think it would be likely to ever happen, but it sure would be funny if it did.

You may only play an enhance one per enhance step. The ability says you can, but can't overrides can and the ability doesn't say that it is an exception to the rules like Sakura with two reversals.

Actually, there's no "can't" involved... just once per enhance phase.

302.8.2 [snip] Any copy of an E may only be played once per enhance step...

The "Your opponent may play this ability" isn't an effect saying "OK now that I've played this, you can"... it's text that states the ability may be played by your opponent or yourself. Yeah, it could be worded better but it's an old card and that kind of templating wasn't standard at the time.