Can Modern Nuclear Hamiltonians Tolerate a Bound Tetraneutron?

I show that it does not seem possible to change modern nuclear Hamiltonians to bind a tetraneutron without destroying many other successful predictions of those Hamiltonians. This means that, should a recent experimental claim of a bound tetraneutron be confirmed, our understanding of nuclear forces will have to be significantly changed. I also point out some errors in previous theoretical studies of this problem.