Adding anything to the water will just cause the filter(s) and DI resin to work to remove it from the water. That being said, there are EDM specific cleaners out there that work well. We would typically drain our tank, clean everything, and then refill the system up with water that had been run through a resin bottle from the tap.
If you are machining something that is especially dirty and your filtration system cannot keep up, that is a different story and you can do something about that. Some EDM systems I have used we have added a sock filter to the drain from the EDM tank going into the water system. This will help remove any solids from the water. Alternatively or additionally you can add a settling tank. A settling tank for a wire EDM machine should have enough volume to drain the entire tank into. As the water drains into the settling tank it will overflow into the filtration system. The goal there is to slow the water down and give it time for the solids to fall out.
