This paper addresses a multicriteria problem of integer linear programming with parametric optimality. Parameterization is introduced by dividing a set of objectives into a family of disjoint subsets, within each Pareto optimality is used to establish dominance between alternatives. The introduction of this principle allows us to connect such classical optimality sets as Pareto and extreme. The parameter space of admissible perturbations in such a problem is formed by a set of additive matrices, with arbitraryHölder's norms specified in the solution and criterion spaces. The attainable lower and upper bounds for the radii of quasistability are obtained.