I went through this recently and ran into the same battle. The AC agent said various things "it would be against our procedures" and "we would only take control in an emergency" and the comment that really stopped me in my tracks "you don't want the agent to lose control". They left me with the distinct impression that it would be hugely disadvantageous to me if the agent lost control.

The problem is that our agent was hugely resistant to splitting payment like that. Their system didn't really have a convenient way to handle it and I think they would have difficulty figuring out how to refund it if there was a change. And in fact now I'm considering changing the ticket and wondering if they'll have difficulty figuring out to split any refund or extra due.

In a previous job the agent had no trouble doing this. They charged me an MCO and applied that with the company payment for the PY fare. But that was a very different agency.