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We consider a novel problem where multiple rigid convex polygonal objects rest in randomly placed positions and orientations on a planar surface visible from an overhead camera. The objective is to efficiently grasp and transport all objects into a bin using multi-object push-grasps, where multiple objects are pushed together to facilitate multi-object grasping. We provide necessary conditions for frictionless multi-object push-grasps and apply these to filter inadmissible grasps in a novel multi-object grasp planner. We find that our planner is 19 times faster than a Mujoco simulator baseline. We also propose a picking algorithm that uses both single- and multi-object grasps to pick objects. In physical grasping experiments comparing performance with a single-object picking baseline, we find that the frictionless multi-object grasping system achieves 13.6\% higher grasp success and is 59.9\% faster, from 212 PPH to 340 PPH. See \url{https://sites.google.com/view/multi-object-grasping} for videos and code.