Feature selectivity of visual cortical responses measured during passive fixation provides only a partial view of selectivity because it does not account for the influence of cognitive factors. Here we focus on primate area V4 and ask how neuronal tuning is modulated by task engagement. We investigated whether responses to colored shapes during active shape discrimination are simple, stimulus-agnostic, scaled versions of responses during passive fixation, akin to results from attentional studies. Alternatively, responses could be subject to stimulus-specific scaling, that is, responses to different stimuli are modulated differently, resulting in changes in underlying shape/color selectivity. Among 83 well-isolated V4 neurons in two male macaques, only a minority (16 of 83), which were weakly tuned to both shape and color, displayed responses during fixation and discrimination tasks that could be related by stimulus-agnostic scaling. The majority (67 of 83), which were strongly tuned to shape, color, or both, displayed stimulus-dependent response changes during discrimination. For some of these neurons (39 of 83), the shape or color of the stimulus dictated the magnitude of the change, and for others (28 of 83) it was the combination of stimulus shape and color. Importantly, for neurons with one strong and one weak tuning dimension, stimulus-dependent response changes during discrimination were associated with a relative increase in selectivity along the stronger tuning dimension, without changes in tuning peak. These results reveal that more strongly tuned V4 neurons may also be more flexible in their selectivity, and imbalances in selectivity are amplified during active task contexts.SIGNIFICANCE STATEMENT Tuning for stimulus features is typically characterized by recording responses during passive fixation, but cognitive factors, including attention, influence responses in visual cortex. To determine how behavioral engagement influences neuronal responses in area V4, we compared responses to colored shapes during passive fixation and active behavior. For a large fraction of neurons, differences in responses between passive fixation and active behavior depended on the identity of the visual stimulus. For a subgroup of strongly feature-selective neurons, this response modulation was associated with enhanced selectivity for one feature at the expense of selectivity for the other. Such flexibility in tuning strength could improve performance in tasks requiring active judgment of stimuli.