Large language model (LLM)-based agents rely on memory mechanisms to reuse knowledge from past problem-solving experiences. Existing approaches typically construct memory in a per-agent manner, tightly coupling stored knowledge to a single model's reasoning style. In modern deployments with heterogeneous agents, a natural question arises: can a single memory system be shared across different models? We found that naively transferring memory between agents often degrades performance, as such memory entangles task-relevant knowledge with agent-specific biases. To address this challenge, we propose MemCollab, a collaborative memory framework that constructs agent-agnostic memory by contrasting reasoning trajectories generated by different agents on the same task.