In my opinion, the only way to determine the best option to improve fractionation is to use a calibrated column simulation model to provide reliable guidance. The model calibration must be done against averaged on-line data (gathered over at least a few hours of steady operation, with lab samples gathered for product quality). This is a non-trivial exercise.
Then, running the base model against various cases and simple plotting of the pertinent variables provides great insight.
Options to consider include:
(1) Increase feed preheat
(2) Adjust pumparound / overhead reflux duties to increase internal L/V ratio in the tower section under consideration
(3) Adjust product draw rates
(4) Adjust side-stripper steam
The final answer would likely be a combination of all of the above.
You might also need to run pumparound exchanger rating calculations because, beyond a certain point, increasing circulation does not increase duty appreciably. Also, significant changes in column or furnace loading might require checking against equipment capacity limits (tray hydraulics and furnace tube metal temperature, etc.).
It's a lot of work, but that's what process engineers should do.