The phrase "while agreeing on" is correct and completely usable in written English.
You can use it to indicate that two or more parties are in the process of reaching an agreement. For example: "After extensive negotiations, the company and the union are while agreeing on a new labor contract."
They varied in details while agreeing on a rough outline.
Other people, while agreeing on the event's momentousness, disagreed on the nature of its tidings.
And while agreeing on little else, some in both camps credit Mr. Krupp for breaking the logjam.
While agreeing on the scope of the problem of sprawling development, representatives of the building industry disagree that the solution is more federal money for preserving farmland.
He again urged Congress to adopt a plan that would limit any short-term changes in fiscal policy, while agreeing on long-term steps to reduce the "unsustainable" growth of the federal debt.
While agreeing on the final outline of the budget package, Congressional negotiators said today that they were still trying to hammer out the final details on the appropriations to state and local government for counterterrorism programs.
While agreed on the need to save Florange, the plant's main unions, the CFDT and Force Ouvrière, disagree over how.
And while we won't agree on everything going forward, we agree that Uber's acquisition of Otto could and should have been handled differently.
Here, Yuan et al. predicted 'fuzzy' nucleosome locations, while all other methods agree on well localized short nucleosomes.
"We received full value on the training compensation side, while agreeing to further add on terms," chief executive Duncan Fraser told the club website .
But on Saturday, while agreeing to continue the lifeline, they refused to increase it.
