Sure.
Ability Score Increases, Mythic Feats, Surge, Hard to Kill, Amazing Initiative, Recuperation, Mythic Saving Throws, Force of Will, Unstoppable and Legendary Hero are just 1:1 copies of the mythic rules.
The Personal Essence Pool is just a renamed version of Mythic Power.
Anima Banners are basically strong light-spells, including daylight, which is mostly alright.
But HOLY SHIT Peripheral Essence!
A second-tier Solar has more Essence than a tenth-tier Mythic character has mythic. That's just blatant, utter, devastating power creep.
Just....just no. Nope nope nope nope nope forevereverever.
Just....just being able to spend that much mythic power on surges, initiative and recuperation is utterly broken. The only way this can be maybe-sorta justified is if you make damn sure you can't ever take any normal mythic abilities with this, only dominion abilities, and if you're prepared to deal with that amount of surges.
Okay, at this point you basically have to assess all the Dominion abilities.
And there's a lot of them. Most of them seem to cost several motes, so the concern of "holy shit so much mythic power" might be alleviated. Except there's still surges, some mythic feats, and mythic spellcasting - so the resource allocation there will still be blown out of the water. This could be fixed by turning "personal motes" back into mythic power, and only allowing these things to be fueled by mythic power.
That'd be a lot of work, but the balance there seems to be all over the place.
For example, Dawns get +tier to Intimidate and swift-action multi-intimidate. Twilights get....to not spend a spell slot on mage armor, wohoo!
So can this work? Right now it mostly seems like "mythic, except more complicated and powerful". Which...isn't really a good thing, considering how powerful mythic already gets.