Intensified job demands (IJDs) originate in the general accelerated pace of society and ever-changing working conditions, which subject workers to increasing workloads and deadlines, constant planning and decision-making about one’s job and career, and the continual learning of new professional knowledge and skills. This study investigated how individual characteristics, namely negative and positive affectivity related to competence demands, and multitasking preference moderate the association between IJDs and cognitive stress symptoms among media workers (n = 833; 69% female, mean age 48 years). The results show that although IJDs were associated with higher cognitive stress symptoms at work, that is, difficulties in concentration, thinking clearly, decision-making, and memory, competence demands-related negative affectivity explained the most variance in cognitive stress symptoms. In addition, IJDs were more strongly associated with cognitive stress symptoms at work in individuals with high competence demand-related negative affectivity, and low multitasking preference (moderation effects). Altogether, the present findings suggest that HR practices or workplace interventions to ease employees’ negative affectivity from increasing competence demands at work could usefully support employees’ effective cognitive functioning when confronted with IJDs.