Multifunctional electrocatalysts for oxygen reduction reaction (ORR), oxygen evolution reaction (OER), and hydrogen evolution reaction (HER) are crucial for development of the key electrochemical energy storage and conversion devices, for which single-atom catalyst (SAC) has present great promises. Very recently, some experimental works showed that structurally well-defined ultra-small transition-metal clusters (such as Fe and Co tetramers, denoted as Fe4 and Co4, respectively), can efficiently modulate the catalytic behavior of SACs by axial coordination. Herein, taking the graphene-supported MN4 SACs as representatives, we theoretically explored the feasibility of realizing multifunctional SACs for ORR, OER and HER by this novel axial coordination engineering. Through extensive first-principles calculations, from 23 candidates, IrN4 decorated with Fe4 (IrN4/Fe4) is identified as the promising trifunctional catalyst with the theoretical overpotential of 0.43, 0.51 and 0.30 V for OER, ORR and HER, respectively. RhN4/Fe4 and CoN4/Fe4 are recognized as potential OER and ORR bifunctional catalysts. In addition, NiN4/Fe4 exhibits the best ORR activity with an overpotential of 0.30 V, far superior to the pristine NiN4 SAC (0.88 V). Electronic structure analyses reveal that the significantly enhanced ORR/OER activity can be ascribed to the orbital and charge redistribution of Ni/Ir active center, resulting from its electronic interaction with Fe4 cluster. This work could stimulate and guide the rational design of graphene-based multifunctional SACs realized by axial coordination of small TM clusters, and provide insights into the modulation mechanism.