In a previous article, an algorithm for discovering therapeutic targets in Boolean networks modeling disease mechanisms was introduced. In the present article, the updates made on this algorithm, named kali, are described. These updates are: i) the possibility to work on asynchronous Boolean networks, ii) a smarter search for therapeutic targets, and iii) the possibility to use multivalued logic. kali assumes that the attractors of a dynamical system correspond to the phenotypes of the modeled biological system. Given a logical model of a pathophysiology, either Boolean or multivalued, kali searches for which biological components should be therapeutically disturbed in order to reduce the reachability of the attractors associated with pathological phenotypes, thus reducing the likeliness of pathological phenotypes. kali is illustrated on a simple example network and shows that it can find therapeutic targets able to reduce the likeliness of pathological phenotypes. However, like any computational tool, kali can predict but can not replace human expertise: it is an aid for coping with the complexity of biological systems.