Action 555 (May 1984) sure looks like a story between Superman and Supergirl, with the Parasite being involved to a lesser degree. That’s what the cover implies.
But it is not in any way what Kupperberg, Swan and Hunt deliver. The Parasite does return, and can still track Superman as Clark Kent. The Parasite drains his energy and they fight and fight. Parasite traps Superman to use him as a battery, but Superman breaks free and gets the best of the monster. And all the while one keeps waiting for Supergirl to show up.
She finally does, at the very end. She does have a brief cameo earlier in the story, I will admit that. And the Parasite story, and the Superman/Supergirl team-up does continue into the following issue of Supergirl.
This is a perfect example of the kind of covers I hate, that completely misrepresent a story, and really ought to be the cover for the next chapter of the tale.