As one common precursor for both PM_2.5 and O₃ pollution, NO_<i>x</i> gains great attention because its controls can be beneficial for reducing both PM_2.5 and O₃. However, the effectiveness of NO_<i>x</i> controls for reducing PM_2.5 and O₃ are largely influenced by the ambient levels of NH₃ and VOC, exhibiting strong nonlinearities characterized as NH₃-limited/-poor and NO_<i>x</i>-/VOC-limited conditions, respectively. Quantification of such nonlinearities is prerequisite to making suitable policy decisions but limitations of existing methods were recognized. In this study, a new method was developed by fitting multiple simulations of a chemical transport model (i.e., Community Multi-scale Air Quality Modeling System (CMAQ)) with a set of polynomial functions (denoted as <q>pf-RSM</q>) to quantify responses of ambient PM_2.5 and O₃ concentrations to changes in precursor emissions. The accuracy of the pf-RSM is carefully examined to meet the criteria of a mean normalized error within 2&amp;thinsp;% and a maximal normalized error within 10&amp;thinsp;% by using forty training samples with marginal processing. An advantage of the pf-RSM method is that the nonlinearity in PM_2.5 and O₃ responses to precursor emission changes can be characterized by quantitative indicators, including (1) peak ratio (denoted as PR) representing VOC-limited or NO_<i>x</i>-limited condition, (2) suggested reduction ratio of VOC to NO_<i>x</i> (denoted as VNr) to avoid increasing O₃ under VOC-limited condition, (3) flex ratio (denoted as FR) representing NH₃-poor or NH₃-rich condition, and (4) enhanced benefits in PM_2.5 reductions from simultaneous reduction of NH₃ with the same reduction rate of NO_<i>x</i>. A case study in Beijing-Tianjin-Hebei region suggested that most urban areas present strong VOC-limited condition with PR from 0.4 to 0.8 in July, implying that the NO_<i>x</i> emission reduction rate need be greater than 20&amp;thinsp;%&amp;ndash;60&amp;thinsp;% to pass the transition from VOC-limited to NO_<i>x</i>-limited. A simultaneous VOC control (VNr is about 0.5&amp;ndash;1.2) can avoid increasing O₃ during the transition. For PM_2.5, most urban areas present strong NH₃-rich condition with PR from 0.75&amp;ndash;0.95, implying the NH₃ is sufficiently abundant to neutralize extra nitric acid produced by an additional 5&amp;thinsp;%&amp;ndash;35&amp;thinsp;% of NO_<i>x</i> emissions. Enhanced benefits in PM_2.5 reductions from simultaneous reduction of NH₃ were estimated to be 0.04&amp;ndash;0.15&amp;thinsp;µg&amp;thinsp;m^&amp;minus;3 PM_2.5 per 1&amp;thinsp;% reduction of NH₃ along with NO_<i>x</i>, with greater benefits in July when the NH₃-rich condition is not as strong as in January. Thus, simultaneously reducing NH₃ and VOC emission along with NO_<i>x</i> reduction is recommended to assure the control effectiveness of PM_2.5 and O₃.