Yes, (s)he can. This question is relevant since the Dutch government is investigating whether the Dutch civil code should be changed to include the possibility of a child having more than one parent. However, this legal reform is aimed to loosen to connection between legal and biological parenthood. In this post we’ll discuss the possibility of having multiple biological parents.
One method to create a three-parent-child is the following. From an oocyte we can remove the nucleus, and replace it with the nucleus of another oocyte. The newly recombined oocyte will contain the DNA of two people: the mitochondrial DNA of the first oocyte donor, and the nuclear DNA of the second donor. Subsequently the recombined oocyte can be fertilized by a sperm cell, resulting a zygote with the DNA of three different people. The rationale of this technique is to prevent diseases caused by defects in mitochondrial DNA.
A second, more intriguing method is to create human chimeras. Basically a chimera is an organism which the result of the merger of two, or even more, embryos. We could say this a chimera is the opposite of an identical twin. More important chimeras, including human ones, occur in nature. And if a woman would have had sex with two different shortly after each other, such a chimera could have one mother and two fathers. The chance of this possibility is increased by the fact that sperm can survive up to seven days in the female body, and hence able of fertilizing an oocyte.
Most human chimeras are unaware of their condition, but they could be get into trouble because of this. Lydia Fairchild (an ironic name) was denied motherhood of her own child as result of a paternity test. After some investigation it was discovered that Ms. Fairchild was actually a chimera, and consequently in the possession of two different genomes.
It might happen that a female and a male embryo merge into one single human being. What sex should we assign such person? Or should leave that choice up to that person?
When we are writing down the civil code of space settlements, we have to take these things into account.