  We describe work being done at Baylor University investigating the
possibility of new states of mesonic matter containing two or more
quark-antiquark pairs. To put things in context, we begin by describing the
lattice approach to hadronic physics. We point out there is a need for a quark
model which can give an overall view of the quark interaction landscape. A new
application of the Thomas-Fermi (TF) statistical quark model is described,
similar to a previous application to baryons. The main usefulness of this model
will be to detect systematic energy trends in the composition of the various
particles. It could be a key to identifying {\it families} of bound states,
rather than individual cases. Numerical results based upon a set of parameters
derived from a phenomenological model of tetraquarks are given.
