We report Magnetospheric Multiscale observations of reconnection in a thin current sheet at the interface of interlinked flux tubes carried by converging reconnection jets at Earth's magnetopause. The ion skin depth‐scale width of the interface current sheet and the non‐frozen‐in ions indicate that Magnetospheric Multiscale crossed the reconnection layer near the X‐line, through the ion diffusion region. Significant pileup of the reconnecting component of the magnetic field in this and three other events on approach to the interface current sheet was accompanied by an increase in magnetic shear and decrease in Δβ, leading to conditions favorable for reconnection at the interface current sheet. The pileup also led to enhanced available magnetic energy per particle and strong electron heating. The observations shed light on the evolution and energy release in 3‐D systems with multiple reconnection sites.