Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensions of the Standard Model. In this approach the dynamical breaking of chiral symmetry occurs in two (or more) channels (near polycritical values for coupling constants), giving rise to two (or more) composite Higgs doublets. Two types of models are built for which Flavor Changing Neutral Currents (FCNC) are naturally suppressed. In the first Model I the second Higgs doublet is regarded as a radial excitation of the first one. In the second Model II the quasilocal Yukawa interaction with Higgs doublets reduces at low energies to a conventional local one where each Higgs doublet couples to a definite charge current and its v.e.v. brings the mass either to up- or to down-components of fermion doublets. For the special configuration of four-fermion coupling constants the dynamical CP violation in the Higgs sector appears as a result of complexity of v.e.v. for Higgs doublets.