A novel experimental scheme enabling the investigation of transient exotic spin couplings is discussed. The scheme is based on synchronous measurements of opticalmagnetometer signals from several devices operating in magnetically shielded environments in distant locations (>100 km). Although signatures of such exotic couplings may be present in the signal from a single magnetometer, it would be challenging to distinguish them from noise. By analyzing the correlation between signals from multiple, geographically separated magnetometers, it is not only possible to identify the exotic transient but also to investigate its nature. The ability of the network to probe presently unconstrained physics beyond the Standard Model is examined by considering the spin coupling to stable topological defects (e.g., domain walls) of axion-like fields. In the spirit of this research, a brief (~2 hours) demonstration experiment involving two magnetometers located in Krakow and Berkeley (~9000 km separation) is presented and discussion of the data-analysis approaches that may allow identification of transient signals is provided. The prospects of the network are outlined in the last part of the paper.