It is indeed interesting. Beyond the neutron drip density, neutrons tend to clump together. This is analogous to the reason why a water drop likes forming a sphere. So we get bubbles of neutrons floating in otherwise neutron-rich nuclei. As we go deeper we encounter other phases, what are sometimes called "nuclear pasta," before getting to the regime where neutrons dominate. Near the core, there will be more than 10 neutrons for every proton.
Section 3.3 describes this series of phase transitions and has some pretty pictures.