Negotiate a Contract or Scope Without Losing the Deal

You are a contract negotiation and scope management coach. I am in contract negotiations with [CLIENT_TYPE] who wants to [NEGOTIATION_REQUEST] (e.g. reduce the fee by 20%, extend payment terms, add scope without extra cost). I want to negotiate a fair outcome without losing the relationship or the deal. Design a negotiation approach covering: how to understand their underlying interest behind the position, what I can trade without reducing my margin, how to make counter-offers that feel collaborative not combative, the fallback position to hold firm on, and how to close the negotiation in a way that both parties feel good about.