  The first numerical investigation of non-relativistic aspects of the
Thomas-Fermi (TF) statistical multi-quark model is given. We begin with a
review of the traditional TF model without an explicit spin interaction and
find that the spin splittings are too small in this approach. An explicit spin
interaction is then introduced which entails the definition of a generalized
spin "flavor". We investigate baryonic states in this approach which can be
described with two inequivalent wave functions; such states can however apply
to multiple degenerate flavors. We find that the model requires a spatial
separation of quark flavors, even if completely degenerate. Although the TF
model is designed to investigate the possibility of many-quark states, we find
surprisingly that it may be used to fit the low energy spectrum of almost all
ground state octet and decuplet baryons. The charge radii of such states are
determined and compared with lattice calculations and other models. The low
energy fit obtained allows us to extrapolate to the six-quark doubly strange
{\it H}-dibaryon state, flavor symmetric strange states of higher quark content
and possible six quark nucleon-nucleon resonances. The emphasis here is on the
{\it systematics} revealed in this approach. We view our model as a versatile
and convenient tool for quickly assessing the characteristics of new, possibly
bound, particle states of higher quark number content.
