  Atomic clocks use atomic transitions as frequency references. The
susceptibility of the atomic transition to external fields limits clock
stability and introduces systematic frequency shifts. Here, we propose to
realize an atomic clock that utilizes an entangled superposition of states of
multiple atomic species, where the reference frequency is a sum of the
individual transition frequencies. The superposition is selected such that the
susceptibilities of the respective transitions, in individual species,
destructively interfere leading to improved stability and reduced systematic
shifts. We present and analyze two examples of such combinations. The first
uses the optical quadrupole transitions in a $^{40}$Ca$^+$ - $^{174}$Yb$^+$
two-ion crystal. The second is a superposition of optical quadrupole
transitions in one $^{88}$Sr$^+$ ion and three $^{202}$Hg$^+$ ions. These
combinations have reduced susceptibility to external magnetic fields and
blackbody radiation.
