Abstract This paper is a sequel to the work discussed in Pesterev et al. (Journal of Sound and Vibration, in press). In that paper, it was suggested that the technique to determine the effect of a local road surface irregularity on the dynamics of a vehicle modelled as a linear multi-degree-of-freedom system relies on the so-called pothole dynamic amplification factor (DAF), which is a complex-valued function specific to the irregularity shape. This paper discusses the companion problem of how to determine the DAF function for an irregularity represented as a superposition of simpler ones. Another purpose of this paper is to demonstrate the application of the pothole DAF functions technique to finding a priori estimates of the effect of irregularities with a repeated structure. Specifically, we solve the problem of finding the conditions under which the dynamic effect of two identical potholes located one after another is greater than that due to the single pothole. We also find the estimate for the number of periods of a periodic irregularity that are sufficient in order to consider the oscillator response as steady state. The discussions are illustrated by numerical examples.