Supporting physical exertion is a growing trend in digital technology design. However, most experiences focus on bodily actions in which participants act independently of each other. In contrast, we focus on virtual body-to-body interactions between multiple participants, inspired by combat-oriented sports such as boxing that highlight the need to act while avoiding reciprocal bodily action. Mediating such body-to-body interactions with technology is challenging, particularly when participants are not co-located. Prior systems have often involved a mixture of novel physical interfaces and interactions through virtual avatars. This paper charts a design space for virtual combat play experiences and offers a set of design dimensions and recommendations for future systems. We draw on our experiences of designing and evaluating Remote Impact – a boxing-style exertion game involving aggressive bodily interaction with a large force-sensing projection surface. By expanding our knowledge of mediated exertion with an understanding of combat interactions we extend the social experience space of exertion play.