No. One parent claims the child and all the benefits, the other parent deletes the child completely.
The reason you get that result is by answering "yes" that you have a custody agreement the determines who claims the child. This question does not refer to informal agreements between partners living together, only to divorced or separated parents living apart. If you live together with the other parent you say no, and I think the answer works out right that way. The safer thing is to simply delete the child from the return of the parent who will not be claiming them.
The interview would be clearer if Turbotax asked "do you live together unmarried with the other parent" but a focus group decided the question was "too personal."
