We discuss flavor-chiral grand unifying theories based on semisimple gauge groups. Typical no-go theorems which characterize the SU(N) unification are avoided within the corresponding SU(N)×SU(N) schemes, which furthermore offer a natural generation structure with a fixed number Ng of generations. We classify all such theories which satisfy basic unification requirements, and find 3<=Ng<=7. The most interesting schemes are SU(5)×SU(5)-the minimal multigeneration scheme, SU(7)×SU(7) with a single fermionic representation, and SU(9)×SU(9) for Ng=3. The incorporation of heavy-color interactions in these schemes turns out to be inconsistent with the generation structure in the presence of a residual horizontal symmetry. Pati-Salam-type models, which are flavor-color but not left-right symmetric, are also discussed.