This paper presents a multiple concurrent slotframe scheduling (MCSS) protocol for wireless power transfer (WPT)-enabled wireless sensor networks. The MCSS supports a cluster-tree network topology composed of heterogeneous devices, including hybrid access points (HAPs) serving as power transmitting units and sensor nodes serving as power receiving units as well as various types of traffic, such as power, data, and control messages (CMs). To this end, MCSS defines three types of time-slotted channel hopping (TSCH) concurrent slotframes: the CM slotframe, HAP slotframe, and WPT slotframe. These slotframes are used for CM traffic, inter-cluster traffic, and intra-cluster traffic, respectively. In MCSS, the length of each TSCH concurrent slotframe is set to be mutually prime to minimize the overlap between cells allocated in the slotframes, and its transmission priority is determined according to the characteristics of transmitted traffic. In addition, MCSS determines the WPT slotframe length, considering the minimum number of power and data cells required for energy harvesting and data transmission of sensor nodes and the number of overprovisioned cells needed to compensate for overlap between cells. The simulation results demonstrated that MCSS outperforms the legacy TSCH medium access control protocol and TSCH multiple slotframe scheduling (TMSS) for the average end-to-end delay, aggregate throughput, and average harvested energy.