Gaze-based alternative and augmentative communication (AAC) devices provide users with neuromuscular diseases the ability to communicate with other people through only the movement of their eyes. These devices suffer from slow input, causing a host of communication breakdowns to occur during face-to-face conversations. These breakdowns lead to decreased user autonomy, conversation quality, and communication partner engagement. Attempts to improve communication through these devices has mainly focused on throughput and rate enhancement, though this has only attained meager results to date. In this work, we address this issue from the top down by considering AAC devices as a form of groupware and designing interactions around this groupware that facilitate better conversations for all involved communicators. We first present qualitative findings on issues with gaze-based AAC and end-user communication preferences; we identify several design guidelines for improving these systems and then present AACrobat, a system that embodies these guidelines and introduces novel interactions by extending gaze-based AAC devices with a mobile companion app. Finally, we present early feedback on AACrobat through three case studies of users with ALS.