Do you really think we're in a position to "run" a side at all, let alone strongly?
We would need a clear idea of what a "win" would be. Have we got one?
We can tell the Russians, the Iranians, the Israelis, and the Gulf States any damned thing we please. They can and will tell us to go stuff it, and there will not be a thing we can do about it. What makes you think we're in a position to play the music and expect anyone else to dance? If you tell the Russians, Iranians, Israelis, or Gulf Arabs what to do and they tell you to stick it where the sun don't shine (which they will), what do you do about it?
I can't see how we'd explain that, because it wouldn't benefit us, or the region. You might get the notoriously credulous Americans to go along if you spun them a good enough tale, but why would the rest of the region go along, especially if part of the package is us telling everyone else what to do?
They can't do any of that stuff. They haven't the leverage.
We may not do it, though it looms perilously close. I hope somebody in the picture has the fortitude to just say no, because I can see no upside whatsoever to "going in". We have no clear desired end state, at least none we can reasonably hope to achieve. We haven't the capacity to control our allies or our proxies. We will probably be worked by both. What's to gain?
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