  Continuing our previous analysis of a supersymmetric quantum-mechanical
matrix model, we study in detail the properties of its sectors with fermion
number F=2 and 3. We confirm all previous expectations, modulo the appearance,
at strong coupling, of {\it two} new bosonic ground states causing a further
jump in Witten's index across a previously identified critical 't Hooft
coupling $\lambda_c$. We are able to elucidate the origin of these new SUSY
vacua by considering the $\lambda \to \infty$ limit and a strong coupling
expansion around it.
