We show that the resonance fluorescence spectrum of a quantum dot excited by a strong optical pulse contains multiple peaks beyond those of the Mollow triplet. We show that as the area of the optical pulse is increased, new side peaks split off the central peak and shift in frequency. A simple analytical theory has been derived, which quantitatively accounts for the appearance and position of the peaks. This theory explains the physics responsible for the multiple peaks. By considering the time-dependent spectrum we demonstrate a time ordering of the side peaks, which is further evidence for the suggested physical explanation. © 2012 American Physical Society.