  We present an analysis of excited-state solutions for a gravitationally
localized system consisting of a filled shell of high-angular-momentum
fermions, using the Einstein-Dirac formalism introduced by Finster, Smoller,
and Yau [Phys. Rev. D 59, 104020 (1999)]. We show that, even when the particle
number is relatively low ($N_f\ge 6$), the increased nonlinearity in the system
causes a significant deviation in behavior from the two-fermion case.
Excited-state solutions can no longer be uniquely identified by the value of
their central redshift, with this multiplicity producing distortions in the
characteristic spiraling forms of the mass-radius relations. We discuss the
connection between this effect and the internal structure of solutions in the
relativistic regime.
