If you are required to negotiate for a client you can stand out by being the one that really “fights for your client”.
If your client perceives that you are on their side, working for them, they will reward you handsomely. It my not come in the form that you expect, but if you negotiate a better timeline, save on costs, find a better ay to do something that was not in the original scope your client will be delighted. This is what you are going for -- customer delight -- surprising your client positively by being their partner rather than just a vendor.