When interacting individuals entrain, they begin to speak more like each other. To support research on entrainment in cooperative multi-party dialogues, we have created a corpus where teams of three or four speakers play two rounds of a cooperative board game. We describe the experimental design and technical infrastructure used to collect our corpus, which consists of audio, video, transcriptions, and questionnaire data for 63 teams (47 hours of audio). We illustrate the use of our corpus as a novel resource for studying team entrainment by 1) developing and evaluating team-level acoustic-prosodic entrainment measures that extend existing dyad measures, and 2) investigating relationships between team entrainment and participation dominance.