We argue for a new research direction in emergent communication, combining work on `Conversational Grounding' with Symbol Grounding (SG+CG). We first present the fine-grained and targeted feedback signals provided by Conversational Grounding and discuss the potential advantages of such a combination. We argue that a key factor holding back research in this area is lack of appropriate data, where divergent agents can resolve disagreements and errors, and we propose requirements and methods for new data collections enabling such work.