The biaffine parser of Dozat and Manning (2017) was successfully extended to semantic dependency parsing (SDP) (Dozat and Manning, 2018). Its performance on graphs is surprisingly high given that, without the constraint of producing a tree, all arcs for a given sentence are predicted independently from each other (modulo a shared representation of tokens). To circumvent such an independence of decision, while retaining the O(n 2) complexity and highly parallelizable architecture, we propose to use simple auxiliary tasks that introduce some form of interdependence between arcs. Experiments on the three English acyclic datasets of SemEval 2015 task 18 (Oepen et al., 2015), and on French deep syntactic cyclic graphs (Ribeyre et al., 2014) show modest but systematic performance gains on a near state-ofthe-art baseline using transformer-based contextualized representations. This provides a simple and robust method to boost SDP performance.