Acknowledge the idea first
Say the request makes sense before you say anything about scope. Clients push back when they feel dismissed.
Check it against the agreement
Look at what was agreed and say plainly whether this is inside it. If it is, do it; if not, say so without blame.
Offer a clear price and time
Give the extra work as an option with a cost and a date. Let the client choose, rather than refusing.
Offer a swap when budget is fixed
If the budget cannot move, offer to trade the new item for something already planned.
Confirm in writing
Once agreed, put the change in a short message or updated scope. It protects both sides later.
Spot the pattern
If every project drifts, tighten the scope wording or add a change-request step at the start.