The most popular version of the Third Man argument is that Platonic forms cannot exist because If there is a separate man that accounts for he likeness between John and George, then there is another separate man to account for te likeness between , say, John and the first separated man, and so on ad infinitum.
The argument, it seems fails at the first inference. We might posit a separate “Blondness” to account for the likeness between Barbie and Thor, but no one has ever suggested that Thor is like blondness. It’s hard to see what this would even mean.
That said, Plato does want to preserve a way in which beauty itself is beautiful, and the form of Good is itself desirable and good. But here again there is a clear need to divide this, and it seem like one of the main efforts of the Symposium to divide goods – which are loved and therefore, as Plato sees it, involve lack- and the Good itself, which terminates all desire and so terminates love.