Electrical resistivity ρ, magnetic susceptibility χ and specific heat C of Pr(Rh 1-x Co x ) 2 Zn 20 for 0 ≤ x ≤ 0.89 were measured to study the mechanism of simultaneous superconducting and antiferroquadrupolar (AFQ) transitions at T c = T Q = 0.06 K in PrRh 2 Zn 20 . A broad peak in the magnetic specific heat C m (T) at around 13 K is reproduced as a Schottky peak by a doublet-triplet two-levels model. However, another broad peak in C m (T) at 1 -3 K indicates splitting of the doublet state by a slight distortion of Zn cages due to the Co substitution. As a consequence of the splitting, the quadrupolar degrees of freedom must be quenched. With increasing x, T c = 0.06 K for x = 0 is suppressed below 0.04 K for x ≥ 0.10. The suppression of T c suggests possible interplay between the superconductivity and the quadrupolar degrees of freedom.