For New England, specifically? They'd never accept such control coming from the Crown. They loved England, yes, but not how the Stuarts ran it.
But getting the New England Confederation officially recognized in some form by the Commonwealth/Protectorate, on condition of adding Rhode Island and recognizing the independence of New Hampshire (if under Puritan governing norms) and Lyconia/Maine (again, under Puritan domination) as separate units within it could be done, perhaps (I'm expanding the colonies within it so it's both territorially encompassing all New England and forced to learn to work together as a singular unit, as is the entire point of a Dominion). The Commonwealth Parliament granted patents to Maine under guise of Puritan Lyconia and to Rhode Island, after all, so finding some way to turn that into a full-fledged recognition of New England under SOME central authority - albeit this authority's heads would be entirely New Englander, although the Puritans on both sides of the Atlantic would be fine with that - would be the way to go. Probably need something favorable conceded to the Confederation in order to force them to accept Rhode Island, (independent) New Hampshire, and Lyconia/Maine, to make it work though. Probably trade concessions, though that's easy enough as some form of no tarrifs/imposed duties on trade goods. It might surprisingly tilt slightly more liberal than the expected total Puritan domination to placate the many different sub-groups now in this Confederation (the various royalist sympathizer-settlers in New Hampshire and Lyconia, the religiously-tolerant population of New Plymouth if not its government, Rhode Island in general, Connecticut's slight religious moderation and tolerance) - I would say like Connecticut at the time this NEC allows all Protestant landowners to be active in government even if Congregationalism is the state-sanctioned-and-supported church all must support.
So this expanded United Colonies of New England would be:
1. Massachusetts
2. Connecticut
3. New Plymouth (maybe finally given an official Parlimentarian patent to settle its legal ambiguity once and for all)
4. New Hampshire (once again independent)
5. Rhode Island
6. Lyconia/Maine (Lyconia expanded to encompass all of Maine, including Royalist 'Maine')
7. New Haven (including Long Island - perhaps the same recognition deal as New Plymouth, perhaps absorbed into Connecticut anyway since they had zero legality of recognition even compared to New Plymouth-cum-New England Council)
From there it gradually becomes more and more a full-fledged, if locally-governed, Dominion in all but name and acting as one whole unit in foreign matters re: New France, New Netherland, and the Amerindians. With the Restoration you will likely see a royal governor installed - the NEC even as one cannot afford to piss off the new royal ascendancy - but is still de-facto is forced to play nice to the local General Court for income and political harmony.