Zoomorphic robots could serve as accessible and practical alternatives for users unable or unwilling to keep pets. However, their affective interactions are often simplistic and short-lived, limiting their potential for domestic adoption. In order to facilitate more dynamic and nuanced affective interactions and relationships between users and zoomorphic robots we present AZRA, a novel augmented reality (AR) framework that extends the affective capabilities of these robots without physical modifications. To demonstrate AZRA, we augment a zoomorphic robot, Petit Qoobo, with novel emotional displays (face, light, sound, thought bubbles) and interaction modalities (voice, touch, proximity, gaze). Additionally, AZRA features a computational model of emotion to calculate the robot's emotional responses, daily moods, evolving personality and needs. We highlight how AZRA can be used for rapid participatory prototyping and enhancing existing robots, then discuss implications on future zoomorphic robot development.