Multi-session agents can switch between LLMs to balance performance and inference cost.
Through controlled experiments with multi-session tasks, we uncover behavior transfer: recipients tend to adopt reasoning and action patterns from the models that generated their histories.
This effect is most evident with raw-history transfer but is substantially reduced by summarization.
Based on these findings, we propose Direction- and Authorship-aware Summarization of History (DASH) that preserves stronger-model behavior while minimizing weak-to-strong transfer via summarization.
Experiments with repeated swaps show that DASH outperforms raw-history transfer and naive summarization baselines.
These results suggest that effective multi-model orchestration requires considering not only which model to use, but also which behavioral patterns to carry forward.