Temporal-coupled-mode theory (TCMT) is an important tool that is widely used for analyzing and designing integrated photonic systems that consist of multiple connected resonators. In microresonator systems with wellseparated modes (relatively large free spectral range compared to the modal width), standard TCMT accounts only for the resonant excitation and is known to give excellent results in the weak-coupling limit. In this paper, we reveal a peculiar situation where TCMT breaks down under multiple excitation conditions. As we demonstrate, this can be explained by the destructive and the constructive interference of the excitations associated to the resonant and off-resonant modes respectively. In this case, we show that a multimode TCMT should be employed to account for these effects. Our results thus suggest that, while it is safe to use the standard TCMT under a single excitation, it must be applied with care when multiple excitations are involved.