Vision-based models for robotic grasping automate critical, repetitive, and draining industrial tasks. Existing approaches are typically limited in two ways: they either target a single gripper and are potentially applied on costly dual-arm setups, or rely on custom hybrid grippers that require ad-hoc learning procedures with logic that cannot be transferred across tasks, restricting their general applicability. In this work, we present MultiGraspNet, a novel multitask 3D deep learning method that predicts feasible poses simultaneously for parallel and vacuum grippers within a unified framework, enabling a single robot to handle multiple end effectors. The model is trained on the richly annotated GraspNet-1Billion and SuctionNet-1Billion datasets, which have been aligned for the purpose, and generates graspability masks quantifying the suitability of each scene point for successful grasps. By sharing early-stage features while maintaining gripper-specific refiners, MultiGraspNet effectively leverages complementary information across grasping modalities, enhancing robustness and adaptability in cluttered scenes. We characterize MultiGraspNet's performance with an extensive experimental analysis, demonstrating its competitiveness with single-task models on relevant benchmarks. We run real-world experiments on a single-arm multi-gripper robotic setup showing that our approach outperforms the vacuum baseline, grasping 16% percent more seen objects and 32% more of the novel ones, while obtaining competitive results for the parallel task.