In this work we broaden the amplitude modulation concept applied to the temporal characterization of ultrashort laser pulses with the amplitude swing technique. We theoretically study the effect of diverse types of relative amplitude and phase modulations. This variation of the replicas can be implemented by means of rotating zero-order waveplates to manipulate the delayed pulse replicas produced in a following multi-order waveplate, which can be more practical under certain conditions. We numerically simulate and study different scenarios under different modulations and for different noise levels and pulses. The proposed schemes are validated and compared through the experimental application to compressed and chirped pulses, confirming the applicability of the work. The simplicity, robustness and versatility of this ultrashort pulse measurement benefits the applications of ultrafast optics.