Biopolymers adsorb on cell and virus surfaces with great specificity. Recently, theoretical and computational studies have inquired as to whether there are any universal design strategies that nature employs in order to affect such recognition. Specifically, the efficacy of multifunctionality and quenched disorder as essential design strategies has been explored. It has been found that when random heteropolymers interact with disordered multifunctional surfaces,a sharp transition from weak to strong adsorption occurs when the statistics characterizing the sequence and surface site distributions are related in a special way. The aforementioned studies consider the intersegment interactions to be much weaker than the surface site interactions. In this work we use nondynamic ensemble growth Monte Carlo simulations to study the effect of the competition between frustrating intersegment and segment-surface interactions. We find that as the intersegment interactions become stronger, the transition from weak to strong adsorption occurs at higher surface disorder strengths. This trend is reversed beyond a threshold strength of the intersegment interactions because interactions with the surface are no longer able to ＇＇unravel＇＇ the dominant conformations favored by the intersegment interactions.