Believe it or not, I would have spun off Alexis.
The setup: through a series of moves and counter moves, Blake, Jeff and others finally succeed in getting Alexis ousted from ColbyCo. Alexis is about to leave Denver in disgrace for a second time, when she gets word that a U.S. Senator from Colorado is set to retire (before the end of his current term) due to failing health (possibly dementia). Alexis maneuvers her way into getting appointed to fill his seat, thereby prompting her big move to the REAL center of power in our country: Washington, D.C.
The new series would revolve around Alexis' navigation of the halls of power within our nation's capital, aided by a staff (largely inherited) of younger folks, whose cutthroat antics as they jockey for power and influence would make the Carrington and Colby's shenanigans look amateurish by comparison.
There would be the requisite clashes with other politicians from both houses of government, the different lobbyists (mostly from the oil and gas industries), visiting dignitaries, the Washington elite, the notorious Beltway press, even the current administration at 1600 Pennsylvania Avenue (although, it's probably a given that we would see the president, lol). Alliances would be built and torn down, as Alexis would go to any lengths necessary to carry out her various agendas.
There would also be an attorney from one of Virginia's founding families, who shares a past with Alexis that stretches all the way back to the 1960's, when she first arrived in the U.S. as a young model, before she met Blake Carrington. Married to a mentally unstable woman who has been in and out of several institutions, he has been left to raise his now-adult daughter, who would function as the show's resident young bitch. She would hate Alexis almost instantly, as she sees Alexis as a threat to her closeness with her father. (As a matter of fact, the first-season cliffhanger could be the introduction of her mother, whom she has sprung from yet another asylum, just as her father is ready to propose Alexis.)
And there would be opportunities for humor, something that DYNASTY lacked, with the addition of Alexis' two servants (one female, one male) in her new D.C. townhouse; as well as the introduction, in the first episode, of young Nicole Morell, whose grandfather is Alexis' younger brother. (Remember, this is occurring before Caress' arrival in Denver.). Nicole, or Nikki, is a teenager from London, whose parents were recently killed in an automobile crash, and whose grandparents are incapable of looking after her due to Jeremy Morell's high-pressure job as head of the one of the Hong Kong trading houses. Therefore, it falls upon "Aunt Alexis" to be Nikki's guardian. At first, Alexis isn't quite sure about this arrangement; however, the longer she's with her, the more she sees herself in her. Plus, it's a second chance to be a mother to someone, something she had been denied with her own children with Blake.
Like I said, there would be more humor - not physical humor, but verbal wit. I'd want it to rival the smartest sitcom of its' time in that respect. For the first season, at least, episodes would be more self-contained, with running narrative threads, rather than a full-blown soap, as we would get to know the characters and the world they operate in. There would be requisite crossovers with characters from the mother show (but only characters and stories that would make sense in this environment - we're not gonna just throw Krystle in D.C. just to have her and Alexis catfight in from of the Lincoln Memorial). And we would get to see more dimensions to Alexis' character than that of just rich bitch/vengeful ex-wife particularly in her relationships with the attorney I've mentioned before, her servant/sidekicks and her grand-niece. (In her Television Archive interview, Donna Mills said that Joan Collins told her she'd wished her writers would have written for her the way KNOTS LANDING's writers wrote for Abby. Well, Dame Joan, ask and ye shall receive, lol.)
Bottom line, though: whether she's running an oil company in Denver, or rubbing shoulders with the prime movers and shakers in Washington, D.C., Alexis is, at her core, Alexis: a savvy, beautiful, fashionable woman "of a certain age," who is determined to play with the big boys, and win.