Kap -> KaKap -> KaKaKap -> KaKaKaKap ->...
But as Suppe himself replies, this is a matter of the way to individuate knowledge. For example, when we know that today's temperature x is lower than y degree, we have infinitely many knowledge like x<y+1, x<y+2, x<y+3, and so on. If this temperature example is admissible, the infinitely many knowledge obtained from the KK thesis may be admissible, too.
2 There are other replies to these difficulties by weakening the notion of knowledge. For example, Hilpinen tries a weak definition of knowledge "Kap <-> Jap & p", in which "a knows that p" does not imply that "a believes that p". This avoids above problems nicely. Barense (Barense 1966, cited in Hintikka 1970, 158-159) tries a weak definition "Kap <-> Bap & p" which also avoids the above second difficulty. These are interesting alternatives, but to analyze them goes beyond the scope of this paper.
 My formulation is slightly different from Suppe's, because I think that if one cannot know that P is true, then she cannot know that P, regardless of the status of the KK thesis. This rather follows from Tarski's convention T, i.e. "P is true if and only if P".
 There are other philosophers who see an essential relationship between skepticism and the KK thesis, e.g. Carrier 1974, Hall 1976. Interestingly enough, they all use the same kind of argument as Suppe's one, with exactly the same weak point.
 Maybe Descartes requires the identity of two knowers. If so, Descartes should refuse the possibility that children without self-knowledge can have knowledge. I do not know his position on this matter. My point is that even this much weaker version of the KK thesis does the trick.