Abstract: The focus on conversational systems has recently shifted towards creating engaging agents by inculcating emotions into them. Human emotions are highly complex as humans can express multiple emotions with varying intensity in a single utterance, whereas the conversational agents convey only one emotion in their responses. To infuse human-like behaviour in the agents, we introduce the task of multi-emotion controllable response generation with the ability to express different emotions with varying levels of intensity in an open-domain dialogue system. We introduce a Multiple Emotion Intensity aware Multi-party Dialogue (MEIMD) dataset having 34k conversations taken from 8 different TV Series. We finally propose a Multiple Emotion with Intensity-based Dialogue Generation (MEI-DG) framework. The system employs two novel mechanisms: viz. (i) determining the trade-off between the emotion and generic words, while focusing on the intensity of the desired emotions; and (ii) computing the amount of emotion left to be expressed, thereby regulating the generation accordingly. The detailed evaluation shows that our proposed approach attains superior performance compared to the baseline models.