A late possession request, the seller asking to stay a few extra days after the sale completes, is common enough that a good agent should have a standard way to handle it: a holdover fee, a clear end date, and a written amendment your lawyer reviews, typically within the same $800 to $1,500 range routine legal work runs, rather than a verbal handshake.
Watch whether the agent protects your interests or just tries to keep the deal moving. An agent who treats a possession-date change as a routine item that still needs a lawyer's sign-off is doing it right; one who suggests skipping the amendment to save time is a red flag.
A calm, procedural answer to this exact question is one of the better tests of how an agent will handle any late complication. Get your hand-reviewed valuation from Joel Dyck.