Large Language Model (LLM)-based agents significantly extend the utility of LLMs by interacting with dynamic environments. However, enabling agents to continually learn new tasks without catastrophic forgetting remains a critical challenge, known as the stability–plasticity dilemma.In this work, we argue that this dilemma fundamentally arises from the failure to explicitly distinguish between common knowledge shared across tasks and conflicting knowledge introduced by task-specific interference. To address this, we propose Agent-Dice, a parameter fusion framework based on directional consensus evaluation.Concretely, Agent-Dice disentangles knowledge updates through a two-stage process: geometric consensus filtering to prune conflicting gradients, and curvature-based importance weighting to amplify shared semantics.We provide a rigorous theoretical analysis that establishes the validity of the proposed fusion scheme and offers insight into the origins of the stability–plasticity dilemma. Extensive experiments on GUI agents and tool-use agent domains demonstrate that Agent-Dice exhibits outstanding continual learning performance with minimal computational overhead and parameter updates.