Multifunctional electrocatalysts for hydrogen evolution reaction (HER), oxygen evolution reaction (OER), and oxygen reduction reaction (ORR) are attractive for overall water-splitting, rechargeable metal-air batteries, and unitized regenerative fuel cells. A single-atom catalyst (SAC) may exhibit additional advantages over its nanoparticle counterpart, and already there have been significant advances in the development of bifunctional and trifunctional SACs for HER, ORR, and OER, but great challenges remain for their rational design. Herein, we propose a strategy to realize multifunctional SACs, i.e., modifying unifunctional materials to introduce new active sites on the surface. Specifically, by virtue of the intrinsic excellent HER performance of 1T'-MoS2, we theoretically design multifunctional SACs by anchoring appropriate transition-metal single atoms. Intriguingly, 1T'-MoS2 with supported Co single atoms (Co@MoS2) are demonstrated to be highly active for both OER and ORR with ultralow overpotentials of less than 0.3 V, ascribed to the moderate chemical activity and unique electronic structure of the Co atomic center. Consequently, combining the intrinsic HER activity of 1T'-MoS2, Co@MoS2 is proposed to be promising efficient trifunctional SACs. Further, the phase engineering on SACs is unrevealed and elucidated by comparing the properties of the Co atomic center-supported on 1T'-MoS2 and 1H-MoS2. This work provides a feasible strategy for the design of multifunctional SACs for the renewable and sustainable energy technology and provides an insight into the phase engineering on SACs.