Scanning-tunneling microscopy (STM) combined withelectronspin resonance (ESR) has enabled single-spin spectroscopy with nanoelectronvoltenergy resolution and angstrom-scale spatial resolution, which allowsquantum sensing and magnetic resonance imaging at the atomic scale.Extending this spectroscopic tool to a study of multiple spins, however,is nontrivial due to the extreme locality of the STM tunnel junction.Here we demonstrate double electron-electron spin resonancespectroscopy in an STM for two coupled atomic spins by simultaneouslyand independently driving them using two continuous-wave radio frequencyvoltages. We show the ability to drive and detect the resonance ofa spin that is remote from the tunnel junction while read-out is achievedvia the spin in the tunnel junction. Open quantum system simulationsfor two coupled spins reproduce all double-resonance spectra and furtherreveal a relaxation time of the remote spin that is longer by an orderof magnitude than that of the local spin in the tunnel junction. Ourtechnique can be applied to quantum-coherent multi-spin sensing, simulation,and manipulation in engineered spin structures on surfaces.