This paper expands on a topic that was explored in recent research by P. Darania et al. (2020), in which the multi-step collocation method (MSCM) has been studied for solving FIEs along with their convergence analysis. This study focuses on the analysis of the linear stability and super-convergence of MSCM for a general form of delay function Θ(t), which includes discontinuity points where the solutions exhibit low regularity. In addition, we present the stability region and the super-convergence order with various examples, thereby demonstrating the accuracy and efficiency of this method. Moreover, the super-convergence and stability regions of the MSCM for FIEs with delay, Θ(t) = t − τ , that do not exhibit any points of discontinuity have been investigated in [4]. 2010 Mathematics Subject Classification: 45G05; 45D05; 65L05; 65L20.