We propose the principle of a three-dimensional (3D) nanoelectron system for bistable or four-stable states based on metallic nanodot arrays and HTSC-N-HTSC (HTSC-SNS) junctions, where HTSC denotes the high-temperature superconductor and N is the normal conductor. We consider the possibility of implementing bistable or four-stable operations on the basis of a 3D nanoelectron system through charge interactions between metallic nanodots on the surface of HTSC-SNS junctions. We present a simple classical circuit model without considering single-electron effects between metallic nanodots, where HTSC-SNS junctions are described as a simplified model of Kümmel-Nicolsky theory. Finally, the calculations based on the Monte Carlo simulation for considering single-electron effects between metallic nanodots demonstrate that our classical model is comprehensive enough for describing this system in nature. We provide numerical results for this HTSC 3D nanoelectron system for different relevant device parameters. The results may be applied to nanologic circuits or nanomemories.