I imagine the MU “Dominion” being the Mirror Gamma Quadrant's Federation. In the MU, the “Dominion” is not the Changeling Empire it is here.
Picture this “Dominion” as being a quadrental “clone” of the RU's UFP &/or the Old Republic from SW. The MU “Dominion” certainly wouldn't be called the Dominion as that's it's RU Imperialist counterpart's name.
What would or should the MU “Dominion” be called, as in the MU the “Dominion” would be a noble, democratic Pax Galactica?
The Jem'Hadar would be radically different, if they “exist” there at all. The Vorta would be very different also.
What about the other ΓQ species in the MU?
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I think the MU Dominion would be like the Federation. Changlings,Jem'hadar,vota, and other dominion species be elected to varies aspects of the government.