When a parasitic radiating element is placed in proximity to the driven one, coupling effects could be observed. This article deals with couplings from the perspective of characteristic modes of coupled system (CMs_coupled) and those of isolated driven/parasitic patch (CMs_iso_dri/par). It is found that CMs_coupled could be flexibly controlled by CMs_iso_dri/par. Complex J/K inverters are introduced to characterize couplings between CMs_iso_dri/par and their values are extracted from derived formulas. The requirements on values of these inverters are also derived for effective bandwidth enhancement. Several antenna examples with electric and magnetic couplings are presented for validation. Then a unified design guideline for enhancing gain and bandwidth is proposed. Next, by reducing radiation side lobes and utilizing capacitive coupling of third-order CMs, a patch antenna is effectively enhanced in both gain and bandwidth. Finally, a prototype patch antenna is fabricated to validate all the analysis experimentally.