Word Sense Disambiguation (WSD) is a key task in Natural Language Processing (NLP), aiming to assign the correct meaning (sense) to a word in context. However, traditional WSD systems rely on WordNet as the underlying sense inventory, often differentiating meticulously between subtle nuances of word meanings, which may lead to excessive complexity and reduced practicality of WSD systems in today’s NLP. Indeed, current Pretrained Language Models (PLMs) do seem to be able to perform disambiguation, but it is not clear to what extent, or to what level of granularity, they actually operate. In this paper, we address these points and, firstly, introduce a new large-scale resource that leverages homonymy relations to systematically cluster WordNet senses, effectively reducing the granularity of word senses to a very coarse-grained level; secondly, we use this resource to train Homonymy Disambiguation systems and investigate whether PLMs are inherently able to differentiate coarse-grained word senses. Our findings demonstrate that, while state-of-the-art models still struggle to choose the correct fine-grained meaning of a word in context, Homonymy Disambiguation systems are able to differentiate homonyms with up to 95% accuracy scores even without fine-tuning the underlying PLM. We release our data and code at https://github.com/SapienzaNLP/homonymy-wsd.