Inhibiting responses is a challenge, where the outcome (partly) depends on the situational context. In everyday situations, response inhibition performance might be altered when irrelevant input is presented simultaneously with the information relevant for response inhibition. More specifically, irrelevant concurrent information may either brace or interfere with response-relevant information, depending on whether these inputs are redundant or conflicting. The aim of this study is to investigate neurophysiological mechanisms and the network underlying such modulations using EEG beamforming as method. The results show that in comparison to a baseline condition without concurrent information, response inhibition performance can be aggravated or facilitated by manipulating the extent of conflict via concurrent input. This depends on whether the requirement for cognitive control is high, as in conflicting trials, or whether it is low, as in redundant trials. In line with this, the total theta frequency power decreases in a right hemispheric orbitofrontal response inhibition network including the SFG, MFG, and SMA, when concurrent redundant information facilitates response inhibition processes. Vice versa, theta activity in a left-hemispheric response inhibition network (i.e., SFG, MFG, and IFG) increases, when conflicting concurrent information compromises response inhibition processes. We conclude that concurrent information bi-directionally shifts response inhibition performance and modulates the network architecture underlying theta oscillations which are signaling different levels of the need for cognitive control.