Off the top of my head, the main reason I wouldn't do it is compatibility issues. Certain concentrations of additives can cause precipitation in the TPN, for example. Also, TPN is formulated each day (in the hospital anyhow) based on a patient's labwork. Any changes that need to be made to the electrolyte solution in the TPN should be addressed within the TPN itself, not by adding another line of lytes. If you are piggybacking into the TPN, you are actually suspending the running of the TPN. If you y-site it in, you aren't, but you are still running into concentration/compatibility/acid-base issues.
Unless I were specifically directed to do so by IV therapy AND pharmacy, I would not EVER run anything into a TPN line. The exception to this, of course, is lipids, which we routinely y-site into TPN. If something was VERY off on the labs and needed to be addressed immediately through the IV, I would expect pharmacy to adjust the TPN and send me a new bag, or I would put the needed infusion through another lumen on the PICC or start a new peripheral site.
I'm curious, is this a hypothetical situation, or did you actually experience this in clinicals or at work? I have never seen a patient need any additional electrolytes with TPN that this situation would even come up, though it's not like I am giving TPN on a daily basis at work, so that may just be my own inexperience.
I'm posting a link to a thread that addresses IV questions in general, and TPN in particular. The 5th comment has several links with information about TPN.
Any Good IV Therapy or Nursing Procedure Web Sites
Hope that helps!