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Hidden-order (HO) phase in heavy-fermion superconductor (SC) is an intriguing phenomena. Doping URu₂Si₂ at the Ru sites reveals how factors such as lattice constants, charge carriers, disorder and d- f- electron hybridization influence the HO phase and SC. The effects of M = Co, Ir substitution in URu_2-xM_xSi₂ for low concentrations of x, are interpreted from x-ray diffraction, resistivity, DC magnetic susceptibility, and specific heat measurements. The features from physical property measurements which characterize the gapping of HO phase become vanishingly small with substitution, so that by x = 0.09 the HO phase is not discernible. For Co substitution, the HO and SC phase transition temperatures (T_HO and T_SC) both decrease monotonically with concentration. With Ir, there is a much smaller suppression of T_SC, and a non-monotonic evolution of T_HO with x. The results for M = Co, Ir indicative of a parasitic AFM phase, which has been shown to emerge in the HO region for Rh substitution are discussed. We compare T_HO, T_SC, lattice constants and the magnitude of the HO feature of Co and Ir with reported M = Rh, P, Fe and Re. Our study offer a new insight into various intriguing ordered phases.