Jensen–Mercer’s inequality for weights satisfying conditions as for the reversed Jensen-Steffensen inequality is proved. Several inequalities involving more than one monotonic function with reversed JensenSteffensen conditions are proved. Furthermore, a couple of general companion inequalities related to Mercer’s inequality with reversed JensenSteffensen conditions are presented as well. Applications for the generalization of weighted Ky Fan’s inequality, classical Power Mean, and classical Arithmetic–Geometric–Harmonic Mean inequalities are given as well.