Sustained production of recombinant proteins encoded by extrachromosomal plasmid DNA over long duration is not possible due to reversion of recombinant cells to unproductive plasmid-free cells. Application of antibiotic selection pressure, the most effective measure to overcome this problem, at a constant rate is prohibitively expensive. Nonlinearities in kinetics of recombinant bioprocesses provide an opportunity to possibly improve the time-average performance of these by periodic forcing of feed conditions. This possibility is investigated in this article using the generalized pi -criterion for continuous recombinant cell cultures subject to periodic variations in one or more inputs (feed parameters), viz., dilution rate and feed concentrations of antibiotic and limiting substrate. The two types of antibiotic action considered are: (i) death of plasmid-free cells and (ii) repression of growth of plasmid-free cells. Pertinent analytical observations, which are applicable to continuous processes in general, are made about operations involving periodic forcing of multiple inputs. Where appropriate, analytical expressions are obtained for optimum amplitude ratios, optimum phase differences, and the corresponding maximum improvement in the process performance. The frequency intervals where an improvement in culture performance is guaranteed are identified via numerical illustrations for the two antibiotic types. These illustrations demonstrate that an increase in the number of feed parameters perturbed leads to broadening of the regions in the multidimensional parameter space where forced periodic operations are superior to steady-state operation. The pi -criterion is also employed to investigate if forced periodic operation may enable retention of recombinant cells under conditions where such retention is not possible in a steady-state operation.