The disclosed embodiments relate to a system that passes control of a customer-support conversation among integrations, which are responsible for responding to a customer during the customer-support conversation. During operation, the system receives a message from a source integration, which is presently responsible for responding to the customer during the customer-support conversation, wherein the message includes a pass-control command that passes control of the customer-support conversation to a target integration. In response to the pass-control command, the system passes control of the customer-support conversation from the source integration to the target integration, so that the target integration becomes responsible for responding to the customer during the customer-support conversation.