Chances are they’re afflicted with the "winner’s curse": whenever they reach a deal, they become cursed with the thought that they could have gotten more.
When the other side seeks to change one item, you should express some surprise or disappointment. Explain that if they must make a change, then they must understand that you will want to open up other issues as well. You agreed to a total package. A change on one issue affects the whole package. Are they willing to renegotiate other issues?
If the answer is yes, then the other side was sincere, and you should proceed with the renegotiating. If they reconsider and withdraw the request for change, then they were just testing you. If they insist that they must have this change and no others, you can express dismay, but you must decide whether the adjusted deal has sufficient value for you to agree.