Can I just add more plant food to a seedling's water reservoir?

I have a seedling in a water farm and the reservoir needs 2 gallons. After a week the seedling doesn't drinks virtually none of the water but grows. It feels like a waste of water to just throw it out and put another 2 gallons with a slightly higher nutrient concentration. I buy water from the store so it's expensive. I know I should get a RO filter I plan to in the near future.

I believe the problem with that is the plant has already used some of the nutrients in the water. Just adding more nutrients is a recipe for disaster since you can't be sure of how much of what will you need. While I'm sure it is possible to calculate how much of what you need to add to balance everything back out, in the end it is easier to bite the bullet and change out that whole reservoir.

I always changed out the reservoir every two weeks, mainly on hygiene concerns. If I were to reuse the solution, I would still clean out the res and bucket and probably add a splash of H2O2 to the solution as well as additional nutes, measuring ppm to desired level. The only time I would consider reusing the solution would be at this stage of growth. But as I said, never done it.

The only reason i'm asking is because the cotyledons are getting pretty bright yellow and the P.H. is fine so i'm assuming it needs a higher ppm. I don't want the true leaves to start yellowing as well.

Why don't you post a pic?

you need RO, well water, rain, or bottled drinking water. stay away from tap. Tap water will work for a while but it has too many buffers the plants will never use. These buffers will constantly raise the pH to higher than you want.

stay away from tap.