Hyperentanglement is a promising resource in quantum information processing, especially for increasing the channel capacity of long-distance quantum communication. Here we present a general hyper-entanglement concentration protocol (hyper-ECP) for nonlocal partially hyperentangled Bell states that decay with the interrelationship between the polarization and the spatial-mode degrees of freedom of two-photon systems, which is not taken into account in other hyper-ECPs, resorting to the optical property of the quantum-dot spins inside one-side optical microcavities. We show that the success probability of our hyper-ECP is largely increased by iteration of the hyper-ECP process. Our hyper-ECP can be straightforwardly generalized to distill nonlocal maximally hyperentangled N-photon Greenberger-Horne-Zeilinger (GHZ) states from arbitrary partially hyperentangled GHZ-class states.