<p>The present work delves into the off-center collision of two compound droplets in an initially at-rest surrounding fluid. The research results reveal four collision interaction modes between two compound droplets: shell coalescence (SC), complete coalescence (CC), bouncing (B), and passing-over (P). The bouncing mode switches to the complete coalescence mode (CC) as increasing the Weber number or decreasing the Reynolds number. An increase in the collision parameter <i>b</i>/<i>R</i>_<i>shell</i> (the distance between the droplets measured in the direction normal to the colliding direction) leads to a mode transition sequence: SC-CC-SC-B. Furthermore, the droplet distance along the colliding direction (<i>S</i>_<i>c</i>) triggers a mode transition from CC to SC. Besides determining the interaction modes between two compound droplets, the study also sheds light on the influence of some parameters on the merging time during the coalescence process. A comprehensive diagram illustrating the interaction modes is proposed to consider the influence of the Weber number, <i>b</i>/<i>R</i>_<i>shell</i>, and the size of the core droplets.</p>