We report a comprehensive phase diagram of the antiferromagnetic Kondo-lattice compound CeRhAl₄Si₂ down to 0.3 K by investigating electrical resistivity, magnetoresistivity, and Hall resistivity under the magnetic field along the c axis. At zero field, CeRhAl₄Si₂ undergoes two successive antiferromagnetic transitions at T_N1=14.2K and T_N2=8.4K, respectively. Upon applying magnetic field, the first-order transition of T_N2 is continuously suppressed at the critical field of 5.5 T. On the other hand, the smooth suppression of the second-order transition of T_N1 terminates at a tricritical point of 6.6 T and 4.7 K, followed by a first-order transition line and an additional phase transition line, which are monotonically suppressed at 6.7 and 7.2 T, respectively, implying the field-induced multiple quantum phase transitions. Particularly, in the paramagnetic region before the Fermi liquid behavior is fully developed, a quantum critical phase with non-Fermi liquid behavior is revealed, indicating a potential spin liquid state that was predicted from the global quantum phase diagram. These results suggest that CeRhAl₄Si₂ is a promising candidate to study a quantum phase transition that occurs in electronic systems with high degree of frustration.