In the outside world, response selection often requires the processing of information from different spatial dimensions. Yet, most neuroscientific approaches to the topic only employ variations in one dimension, namely the horizontal left-right axis. Hence, virtually nothing is known about the neuronal mechanisms underlying response selection in more than one dimension. We investigated this aspect with the help of a two-dimensional flanker task using EEG and source localization techniques. The data shows that response selection processes are differentially modulated across different dimensions. However, this modulation is restricted to conditions imposing increased demands on response selection. In such situations, a distributed fronto-parietal network mediates intensified conflict monitoring processes as well as response inhibition processes. In case response selection is carried out in the horizontal dimension, those brain areas are more active than during response selection in the vertical dimension. Attentional selection processes were not affected. The study's findings are of relevance to our understanding to everyday functioning where response selection is usually carried out in two or three dimensions and not a single dimension as usually investigated in cognitive neuroscience.