  The SYK model: fermions with a $q$-body, Gaussian-random, all-to-all
interaction, is the first of a fascinating new class of solvable large $N$
models. We generalize SYK to include $f$ flavors of fermions, each occupying
$N_a$ sites and appearing with a $q_a$ order in the interaction. Like SYK, this
entire class of models generically has an infrared fixed point. We compute the
infrared dimensions of the fermions, and the spectrum of singlet bilinear
operators. We show that there is always a dimension-two operator in the
spectrum, which implies that, like in SYK, there is breaking of conformal
invariance and maximal chaos in the infrared four-point function of the
generalized model. After a disorder average, the generalized model has a global
$O(N_1) \times O(N_2) \times \ldots\times O(N_f)$ symmetry: a subgroup of the
$O(N)$ symmetry of SYK; thereby giving a richer spectrum. We also elucidate
aspects of the large $q$ limit and the OPE, and solve $q=2$ SYK at finite $N$.
