[pandaman]

Sure, you can almost always ask (everywhere you read they will tell you it's completely safe though it depends on industry, I guess, I have seen offers rescinded over mere asking) however if you are not prepared to walk away there is little incentive to offer what you are asking.

An agent who maintains long relationship with you might actually be ready to negotiate on your behalf since it will both strengthen your relationship and bring quite a lot of money in the future as it increases your base price in all the future negotiations. Third party recruiter placing FTEs, on the other hand, has much to lose by walking away and very little to gain.