A wide range of harmonics especially continuum harmonics is a prerequisite for attosecond pulse generation. One can use longer-wavelength lasers to push the cutoff to a higher order. However, this does not translate to the same amount of continuum range extension because multiple rescattering phenomena are also enhanced in the process, potentially affecting the lower end of the continuum harmonics. It is then important to understand exactly how multiple rescatterings affect the harmonic structure and their response to various laser parameters, which is the main theme of this paper. Particularly, by applying the synchrosqueezed time-frequency transform and classical electron trajectory analysis to the asymmetric molecule carbon monoxide (CO), we justify that the multiple rescatterings indeed influence the periodicity of the harmonic spectra and the stable periodicity is, in fact, bounded by the first- and third-order returns. Moreover, for the first time, we find that the high-order rescatterings are asymmetric regarding the molecular rotation of 180°, but always correlate with the first-order returns. Our last result is that by breaking the laser symmetry in an appropriate way, the contribution of multiple rescatterings is removed so that the continuum region is entirely defined by the first-order return energies.