When a voice agent hands a caller over to another agent, what should actually carry over?

This is something we've been working on at Vaani AI @Vaani Developer Platform . We wanted to solve a simple but important problem: a caller shouldn't feel like they're starting a new conversation every time the system switches agents.

The challenge is that passing a summary isn't always enough. Small but important details can get lost, like a callback time, a promise made earlier, the caller's language preference, or the context behind a decision.

At Vaani, we've been working on making agent handoffs more seamless, so the next agent can pick up the conversation without making the caller repeat themselves or creating a disconnected experience.

But there's still an interesting design question here. How much context should move between agents? Should every agent have access to the full conversation, or should each handoff carry only the relevant context?

Curious to hear how others building multi-agent voice systems are approaching this. What has worked best in production?