Background: The observed mass excesses of analog nuclear states with the same mass number A and isospin T can be used to test the isobaric multiplet mass equation (IMME), which has, in most cases, been validated to a high degree of precision. A recent measurement (Kankainen et al., Phys. Rev. C 93 041304(R) (2016)) of the ground-state mass of 31 Cl led to a substantial breakdown of the IMME for the lowest A = 31, T = 3/2 quartet. The second-lowest A = 31, T = 3/2 quartet is not complete, due to uncertainties associated with the identity of the 31 S member state.Purpose: To populate the two lowest T = 3/2 states in 31 S and use the data to investigate the influence of isospin mixing on tests of the IMME in the two lowest A = 31, T = 3/2 quartets.Methods: Using a fast 31 Cl beam implanted into a plastic scintillator and a high-purity Ge γ-ray detection array, γ rays from the 31 Cl(βγ) 31 S sequence were measured. Shell-model calculations using USDB and the recently-developed USDE interactions were performed for comparison.Results: Isospin mixing between the 31 S isobaric analog state (IAS) at 6279.0(6) keV and a nearby state at 6390.2(7) keV was observed. The second T = 3/2 state in 31 S was observed at Ex = 7050.0(8) keV. Calculations using both USDB and USDE predict a triplet of isospin-mixed states, including the lowest T = 3/2 state in 31 P, mirroring the observed mixing in 31 S, and two isospin-mixed triplets including the second-lowest T = 3/2 states in both 31 S and 31 P.Conclusions: Isospin mixing in 31 S does not by itself explain the IMME breakdown in the lowest quartet, but it likely points to similar isospin mixing in the mirror nucleus 31 P, which would result in a perturbation of the 31 P IAS energy. USDB and USDE calculations both predict candidate 31 P states responsible for the mixing in the energy region slightly above Ex = 6400 keV. The second quartet has been completed thanks to the identification of the second 31 S T = 3/2 state, and the IMME is validated in this quartet.