Few years ago, O'Grady introduced the notion of modular sheaves on hyperkähler manifolds, which, along with the notion of hyperholomorphic and atomic sheaves, aims to a better study of the moduli space of sheaves on hyperkähler manifolds. This led to the need of concrete examples of non-rigid modular vector bundles, which were found by Fatighenti and later by O'Grady. In this talk, I will explain how to replicate on a general Debarre-Voisin manifold a classification of modular vector bundles discovered by Fatighenti and Onorati on the Fano variety of lines on a general cubic fourfold. In particular, I will explain some unexpected relations between similar modular vector bundles over different realizations of hyperkähler manifolds of K3[2]-type. This is a joint work with Federico Tufo.