There certainly has been a large amount of development of modal logic interpretations of Quantum Mechanics. Once you have a Kripkean accessibility relationship (induced from nonorthogonality), the development is simple. Early work here is Goldblatt - "Semantic analysis of orthologic" Journal of Philosophical Logic (1974) and "The Stone space of an ortholattice" Bulletin of the London Mathematical Society (1975), and Dalla Chiara - "Quantum logic and physical modalities" Journal of Philosophical Logic (1977) and "Physical implications in a Kripkean semantical approach to physical theories" Logic in the 20th Century (1983). The basic idea to obtain the accessibility relations uses work from Foulis and Randall on lexicographic orthogonality, as it's not so simple to avoid what would become "extended probabilities" in a counterfactual view of separated events to build the modal relationship.
It is important to make some distinctions with the work described on the page you linked. That research programme is linked with modality in the view of possibilities as a means of regaining realist foundations. That's an involved program that delves into operationalist interpretations and can indeed be used to build modal operators as one is familiar with in modal logic. In fact, there are S4 interpretations on the surface of most operationalist approaches. However, that is not quite the same things as the modal operators of the quantum events themselves, based on the standard orthomodular logical foundation. My first paragraph deals with the latter program.