Task arithmetic has recently emerged as a promising method for editing pre-trained open-vocabulary models, offering a cost-effective alternative to standard multi-task fine-tuning. However, despite the abundance of closed-vocabulary models that are not pre-trained with language supervision, applying task arithmetic to these models remains unexplored. In this paper, we deploy and study task addition in closed-vocabulary image classification models. We consider different pre-training schemes and find that weight disentanglement - the property enabling task arithmetic - is a general consequence of pre-training, as it appears in different pre-trained closed-vocabulary models. In fact, we find that pre-trained closed-vocabulary vision transformers can also be edited with task arithmetic, achieving high task addition performance and enabling the efficient deployment of multi-task models. Finally, we demonstrate that simple linear probing is a competitive baseline to task addition. Overall, our findings expand the applicability of task arithmetic to a broader class of pre-trained models and open the way for more efficient use of pre-trained models in diverse settings.