New Electronic Phase Transitions in \alpha-(BEDT-TTF)2KHg(SCN)4

\alpha-(BEDT-TTF)2KHg(SCN)4 is considered to be in the charge-density-wave (CDW) state below 8 K. We present new magnetoresistance data suggesting that the material undergoes a series of field-induced CDW (FICDW) transitions at pressures slightly exceeding the critical pressure Pc at which the zero-field CDW state is destroyed. Further, we argue that a novel kind of FICDW transitions, entirely determined by a superposition of the strong Pauli and quantizing orbital effects of magnetic field on the CDW wavevector, arises when the field is strongly tilted towards the conducting layers. These new transitions can take place even in the case of a relatively well nested Fermi surface. Finally we report on the superconducting (SC) state and its coexistence with the CDW in the title compound under quasi-hydrostatic pressure. Below Pc the material is most likely a heterogeneous SC/CDW mixture, with the SC phase persisting down to ambient pressure. The SC onset temperature appears to drastically increase upon entering the SC/CDW coexistence region.