Such a scenario will be possible in the near future.
In light of news reports like this one, some people will be worrying that the “institution of reproduction” is under assault.
Others will worry about whether that should that be the government’s business. If you’re willing to pay to utilize such advanced DNA techniques, by what right should the state be able to stop you?
In a piece titled “The Bioethics of a Three-Parent Embryo,” Wired interviews University of Pennsylvania bioethicist Jonathan Moreno about these issues, and he zeroes right in on possible political considerations:

There are going to be a lot of techniques that offer people in gay couples the chance to reproduce in non-traditional ways. This is one possible pathway. We are going to be facing some very interesting social questions about how far this goes.
The two papers published last fall on induced pluripotent stem cells — very few people have noticed that if you can turn a skin cell into a pluripotent cell, and then into a pancreatic cell, you can probably also turn it into sperm cell, or an egg cell, or even a blastomere.
The [Newcastle technique] is one pathway that gives an option for people who either medically or situationally can’t engage in sexual reproduction in traditional way. The key element here is that it lets them use their own DNA.

My body, my blastomere? Or does it cease to be “mine”? Ethicists will haggle, but suppose all I want is a new liver?
Suppose a guy and his wife want the DNA of himself, his wife, and all their best friends scrambled Mixmaster style to create a child with five or six parents and they all consent. Is that the business of others? If so, on what basis?
Is it “conservative” to want the government kept out, or is that liberal?

We’re not in a good position to tell people how to have kids.
But we are in a position to say it’s an area where the public doesn’t want to invest — and that decision was already made 28 years ago in the US with IVF research. And the result of that is that if government isn’t involved early on in the research, it doesn’t have an opportunity to set ethical standards.
That’s one of the ironies about IVF and stem cells — it’s partly because the U.S. government pulled out in 1980 from IVF research that the fertility field developed on its own. And now there’s lots of concern about its practices and standards. That’s the downside of not geting involved. [People who are morally opposed to this] shouldn’t support this necessarily — but the political system kind of controls it.
[If goverment funds the research] then you create a culture of responsibility around that technology. It wouldn’t be perfect or foolproof — but people would have a sense of where they could go, where it would not be acceptable to go. Whereas if you say, “It’s a matter for the market to decide,” the boundary conditions are a lot fuzzier.
It puts bioconservatives in a very odd position: if they say no to government funding, they leave open the possibility of creating a Wild
West scenario. But if they shrug shoulders and say government has to get into this to create a moral culture down the road, then they look as though they’re endorsing it.

Bioconservative?
Yes, there is such a creature!

Bioconservatives are individuals whom oppose human augmentation, whether cybernetic, genetic, or nanotechnological, as opposed to transhumanist whom advocate self-modification.

I don’t seem to have written about the phenomenon before, but I think I’m probably a bioliberal at heart.