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The effect of moderate nonmagnetic chemical substitution of Ir and Rh in α-RuCl₃ is investigated. Single crystals are grown with nominal 10% Ir and 10/20% Rh substituted at the magnetic Ru site. The atomic radii of the nonmagnetic substituted atoms are similar in size to Ru. Neutron diffraction reveals little structural change of the local RuCl₆ environment. In both variants, a room temperature C2/m to low temperature R-3 phase transition is observed with a large recoverable hysteresis like the parent. At the base temperature of 5K, a zigzag magnetic spin order is observed with the same characteristic wavevector (0,0.5,1) present it the parent α-RuCl₃. Magnetic structure refinement of the 10% Ir-substituted sample reveals an ordered moment of 0.32(5) µB/Ru ion and canting angle with upper boundary of 15(4)° which is different from previous reports in the parent α-RuCl₃. The undistorted octahedra environment, reduced magnetic moment size and canting angle indicate the potential to investigate quantum spin liquid behavior through non-magnetic ion doping and presents an attractive approach for tailoring the magnetic properties of materials proximate to a quantum spin liquid state.