Hello Jonas,
To start generally, you may need to look into the operating variables on the control system and see that if the plant is currently at its nominal design production rate where is it limited (restrictions, or bottlenecks) in terms of variables meeting set points, control valves not being too far or too low opening for "control", and also that the process output streams are within the quality or composition targets.
If all seems well then you could arrange some plant trials to move up the production flowrate a little and monitor over a few days what happens. Your plant might or might not be at its actual capacity.
Keep in mind that even if you demonstrate a higher production rate is ok, that conclusion may differ in different seasons (temperature), or with different feed composition, or different level of fouling in the heat exchangers etc.
Dazzler