Using first-principles density functional theory calculations, combined with a topological analysis, we have investigated the electronic properties of Cd 3 As 2 and Na 3 Bi Dirac topological semimetals doped with nonmagnetic and magnetic impurities. Our systematic analysis shows that the selective breaking of the inversion, rotational, and time-reversal symmetry, controlled by specific choices of the impurity doping, induces phase transitions from the original Dirac semimetal to a variety of topological phases such as topological insulator, trivial semimetal, nonmagnetic and magnetic Weyl semimetal, and Chern insulator. The Dirac semimetal phase can exist only if the rotational symmetry C n with n> 2 is maintained. One particularly interesting phase emerging in doped Cd 3 As 2 is a coexisting Dirac-Weyl phase, which occurs when only inversion symmetry is broken while time-reversal symmetry and rotational …