It sounds like you are negotiating pricing of individual claims after the fact and not negotiating contracts with payers. If that's the case, you are in a position of strength because these are services that have already been performed and the money is owed, so you do not need to bend too much. The companies that do these out-of-network negotiations are getting a cut from any money they can save the insurance companies, so of course they will try to get you to come down as much as possible. In my experience, if you counter with a different amount, they will almost always accept it since getting some discount is better than none at all.
The question you should ask is what is the advantage that they are offering you in return for this discount? Usually, they're offering one or both of the following things: a prompt payment and/or payment at an in-network benefit level. Remember that since you're out of network, the insurance may pay less money to you, but the patient will still owe the full amount. So accepting these discounts can be beneficial to your patient too, which can certainly help you with patient satisfaction and ease of collection.
So you should ask yourself, or your manager and provider, would they rather have these things, or would they rather stick to their price and see how the insurance company is going to pay and then be tasked with the efforts of collecting any extra amounts from the patients. It will really depend on the services you are performing, your patient population, and the expectations you've set for your out-of-network patients as to what they understand they're going to owe. At the practice where I used to handle these, we decided that based on where our fees were set, a 20% discount off of our fees was worthwhile (because this was still better than what our in-network payers allowed, and was similar to the self-pay discounts we offered anyway). So this is what I always made as a counter-offer, and as best I recall, they almost always accepted this. I would certainly not accept the low offers they send to you in the first round. There's no reason you have to go along with that.