The identification of optimal intervention strategies is a key step in designing microbial strains with enhanced capabilities. In this paper, we propose a general computational procedure to determine which genes/enzymes should be eliminated, repressed or overexpressed to maximize the flux through a product of interest for general kinetic models. The procedure relies on the generalized linearization of a kinetic description of the investigated metabolic system and the iterative application of mixed-integer linear programming (MILP) optimization to hierarchically identify all engineering interventions allowing for reaction eliminations and/or enzyme level modulations. The effect of the magnitude of the allowed changes in concentrations and enzyme levels is investigated, and a variant of the method to explore high-fold changes in enzyme levels is also analyzed. The proposed framework is demonstrated using a kinetic model modeling part of the central carbon metabolism of E. coli for serine overproduction. The proposed computational procedure is a general approach that can be applied to any metabolic system for which a kinetic description is provided.