This paper proposes a cooperative clustering protocol based on the low energy adaptive clustering hierarchy approach to enhance the longevity of energy harvesting-based wireless sensor networks (EH-WSN). In the proposed protocol, to ensure that any energy consumption associated with the role of the cluster head (CH) is shared between the nodes, the CH role is alternated between the nodes using duty cycling as a function of their individual energy harvesting capabilities. Furthermore, to maintain an energy neutral operation when not acting as a CH, the nodes adopt a data transmission duty cycle and any excess energy is invested in relaying other nodes' packets. To optimize the relaying performance, a novel cross-layer cooperative TDMA scheme is also presented. The optimal number of clusters in an EH-WSN is analyzed in terms of energy consumption, latency, and bandwidth utilization. Simulations, performed using GreenCastalia, demonstrate tangible performance enhancements in adopting the proposed protocol over benchmark schemes in terms of throughput and lifetime, particularly under highly constrained energy conditions.