This study examines the structural stability, electronic, and magnetic properties of off-stoichiometric Zn$_2$Ru$_{1−x}$A$_x$Mn Heusler alloys (with, A = Ti, Mn, Co, Zr, and Rh) using first-principles calculations. We find that the L21 phase is more stable than the XA phase across both ordered and disordered configurations. The variations in lattice parameters with off-stoichiometry are attributed to the atomic radii of the dopants. Our results indicate that Zn2Ru1−xAxMn alloys exhibit ferromagnetic metallic behavior, driven primarily by Mn-Mn, Ru-Mn, and A-Mn exchange interactions. These interactions are further analyzed to calculate the Curie temperature using the mean-field approximation. The Curie temperature for Zn$_2$RuMn is found to be approximately 300 K, which increases to 428 K upon Co doping. Our findings suggest that doping provides a means to control the Curie temperature, offering substantial potential for applications in room-temperature magnetocaloric materials and shape memory alloys. This tunability enhances the functional versatility of these alloys, making them promising candidates for future technological applications.