Basement ductwork "sweating" with condensation

While working on some repairs at an elderly relation's home, I was in the basement and noticed moisture on the floor and surfaces in a certain area, and looking up I could see the underside of the main ductwork coming out of the hvac air handler was just *dripping* with condensation. I didn't think it felt particularly humid down there, and there's a dehumidifier in a separate area of the basement, but it's possible it's not working right or isn't sized appropriately for the whole basement area.

In our area it's been very hot and humid lately, so the A/C has been running *alot*, which might account for part of the problem. But does this indicate any potential airflow issue with the ductwork? What's the right course of action here? Insulate the ducts somehow? Or get a larger dehumidifier down there?

Thanks!