Abstract
We discuss those composite models of quarks and leptons with an $\mathrm{SU}(N)$ metacolor group and preons in the complex, anomaly-free, and asymptotically free representations, which do not have spectators with SU(3) \ensuremath{\bigotimes} SU(2) \ensuremath{\bigotimes} U(1) quantum numbers. We find that many of these models can be ruled out independently of the way the chiral (metaflavor) symmetries are realized and the bound states are constructed. The remaining models contain a large number of preons \ensuremath{\sim}100 or more.
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