The dual modification technique earlier proposed for equality-constrained optimization problems aims at avoiding attraction to critical Lagrange multipliers implying the loss of local fast convergence. In this paper, we extend this technique to problems involving inequality constraints. In particular, we analyze two approaches. One tackles directly the inequality-constrained problem at hand, while the second approach employs squared slacks for reformulating the inequality constraints as equalities. Some theoretical justifications for the corresponding two variants of the stabilized sequential programming algorithm equipped with dual modification procedures are provided. Theoretical expectations are supported by promising numerical results.