In this talk, we continue to discuss the intersection of modular correspondences but on the self-product of two Shimura curves. This is partially motivated by a classical work of Kudla-Rapoport for the single Shimura curve case and by the self-product of modular curves case discussed in Baiqing Zhu's talk. Finally, we will discuss a conjecture that generalizes all the mentioned results for general GSpin Rapoport-Zink spaces with vertex levels. This talk is based on a joint work with Baiqing Zhu.