Praseodymium-based cubic compounds with a 4f2 configuration have attracted much attention. In case the crystalline electric field ground state is a nonmagnetic doublet, the magnetic dipole is quenched but electric quadrupole and magnetic octupole become active. In the present proposal, we focused on PrMgNi4 exhibiting a possible nonmagnetic degenerated ground state. The magnetic specific heat Cm/T shows a broad maximum at around 3 K, which can be reproduced by a two-level model with a ground state doublet. Futhermore, on cooling below 1 K, Cm/T approaches a constant value, which is explained by a random two-level model. Thereby, the twofold degeneracy could be lifted by symmetry lowering due to excess Mg atoms substituted for Pr atoms or the strong c-f hybridization. Inelastic neutron scattering must be a suitable probe to reveal the origin of the hindered long-range quadrupole ordering.