In sentences with a complex subject noun phrase, like "The key to the cabinets is lost", the grammatical number of the head noun (key) may be the same or different from that of the modifier noun phrase (cabinets). When the number is the same, comprehension is usually easier than when it is different. Grammatical number computation may occur while processing the modifier noun (integration phase) or while processing the verb (checking phase). We investigated at which phase number conflict and plausibility of the modifier noun as subject for the verb affect processing, and we imposed a gaze-contingent tone discrimination task in either phase to test whether number computation involves executive control. At both phases, gaze durations were longer when a concurrent tone task was present. Additionally, at the integration phase, gaze durations were longer under number conflict, and this effect was enhanced by the presence of a tone task, whereas no effects of plausibility of the modifier were observed. The finding that the effect of number match was larger under load shows that computation of the grammatical number of the complex noun phrase requires executive control in the integration phase, but not in the checking phase.