Berkshire is right - in a 50 yr old building the source of humidity is either coming from the occupied space above, from condensation on poorly insulated cold water pipes, or leaky pipes (or all of the above). If you're only treating the symptom, you basically have to figure out the volume of...
If this is a VAV system you'll definitely want to pay attention to how the fans are controlled. These will modulate to maintain a static pressure set point from one sensor. You could come up with a control scheme that allows the fans to "know what the other is doing", however if you're using...