  We exhibit examples of slope-stable and modular vector bundles on a
hyperk\"ahler manifold of K3$^{[2]}$-type which move in a 20-dimensional family
and study their algebraic properties. These are obtained by performing standard
linear algebra constructions on the examples studied by O'Grady of (rigid)
modular bundles on the Fano varieties of lines of a general cubic 4-fold and
the Debarre-Voisin hyperk\"ahler manifold.
