Vibro-impact systems are central to many engineering applications, including energy harvesting; yet, unlike smooth dynamical systems, they still lack broadly applicable methods for global dynamical analysis. We develop a novel word-based first-return map framework to study the global dynamics of a vibro-impact pair, modeled as a ball moving up and down inside a harmonically forced capsule. Because impacts define the system’s evolution through discrete collision events, symbolic dynamics provides a natural representation. We encode impacts with the bottom and top of the capsule as B and T, respectively, and describe trajectories through finite words formed from these symbols. In our recent work (Bao et al., SIAM Journal on Applied Dynamical Systems, 24 , 1891, 2025), we focused on short word sequences associated with 1:1 responses (e.g., BTB). Here, we extend the approach to longer words (e.g., BTBB and BBTB) to capture regimes in which 1:1 and 2:1 solutions coexist. This extension demonstrates that the word-based first-return map remains effective in more complex settings and can be used to identify basins of attraction in bi-stable regimes. Moreover, by characterizing the global dynamics of energetically favorable states in the bi-stable regime, we identify parameter regions that maximize energy output in vibro-impact systems and clarify how noise may play a constructive role by triggering switches from low-output to high-output attractors.