Although research indicates that single parenting is not by itself worse for children than their being brought up by both their parents, there are reasons why it is better for children to have more than one committed parent. If having two committed parents is better, everything else being equal, than having just one, I argue that it might be even better for children to have three committed parents. There might, in addition, be further reasons why allowing triparenting would benefit children and adults, at least in some cases. Whether or not triparenting is on the whole preferable to bi- or monoparenting, it does have certain advantages (as well as shortcomings) which, at the very least, warrant its inclusion in debates over the sorts of family structures we should allow in our societies, and how many people should be accepted in them. This paper has the modest aim of scratching the surface of this wider topic by challenging the necessity of the max-two-parents framework.