Recent advances in multi-agent systems have shown great potential for solving complex tasks. However, when multiple agents edit a shared codebase concurrently, their changes can silently conflict and inconsistent views lead to integration failures. Existing multi-agent systems address this through workspace isolation (e.g., one git worktree per agent), but this defers conflict resolution to a post-hoc merge step where recovery is expensive. In this paper, we propose STORM, i.e., STate-ORiented Management for multi-agent collaboration. Specifically, STORM manages agent states by mediating their interactions with the shared workspace, ensuring that each agent operates on a consistent view of the codebase and that conflicting edits are detected and resolved at write time. We evaluate STORM on Commit0 and PaperBench across multiple LLMs. STORM outperforms the git-worktree-based multi-agent baseline by +18.7 on Commit0-Lite and +1.4 on PaperBench, while achieving comparable or better cost efficiency. Combined with single-agent runs, STORM reaches highest scores of 87.6 and 78.2 on the two benchmarks respectively, suggesting that explicit state management is a more effective foundation for multi-agent collaboration than workspace isolation. STORM can also be plugged into any multi-agent system seamlessly.