Think about the customer's view as well. They should not feel pushed between an automated reply and a person with no warning. We write a plain handoff message that says a team member will take over and, where possible, when. That honesty tends to matter more to customers than whether the first reply came from a person.
If your team already answers customers in Intercom, the agent does not need to replace that. It can take the first line of questions and pass the rest into the inbox, so your staff continue in the tool they know. The conversation history travels with the handoff, which saves the customer repeating themselves.
Draw the boundary with your support lead. Simple how-to and policy questions can stay with the agent. Account-specific issues, complaints and billing disputes go to a person. We map those rules to the routing you already have, for example by team or topic, and agree how a handed-off conversation is labelled. Existing help articles are often the best source of approved answers. If they are out of date, the agent will repeat what is wrong, so review them first.
Look at what share of conversations the agent resolves without staff, how many arrive in the inbox with useful context, and which questions keep returning. Repeated questions often point to a gap in the product, the docs or the onboarding, and are worth sharing with the people who own those.