In the transition era towards connected autonomous vehicles (CAVs), the sharing of the roadway by CAVs and human-driven vehicles (HDVs) in a mixed-traffic stream is expected to pose safety and flow efficiency concerns even though CAVs may tend to adopt rather conservative maneuvering policies. Unfortunately, this will likely cause HDV drivers to unduly exploit such conservativeness by driving in ways that imperil safety. A context of this situation is lane-changing by the CAV, a potential major source of traffic disturbance at multi-lane highways that could impair their traffic flow efficiency. In dense, high-speed traffic conditions, it will be extremely unsafe for the CAV to change lanes without cooperation from neighboring vehicles in the traffic stream. To help address this issue, this paper developed a framework through which connected HDVs (CHDVs) could cooperate to facilitate safe and efficient lane-changing by the CAV. A numerical experiment was carried out to demonstrate the efficacy of the framework. The results indicated the CAVs’ lane-changing feasibility and the overall duration of the lane-changing if the CAV carries out that maneuver. It was observed that throughout the lane-changing process, the safety of not only the CAV but also of all neighboring vehicles, was promoted through the framework’s collision avoidance mechanism. The overall traffic flow efficiency was analyzed in terms of the ambient level of CHDV–CAV cooperation. Overall, the results of the study present evidence of how CHDV–CAV cooperation can help enhance the overall system efficiency.