There is an unpublished manuscript "Set Theory for a Small Universe I. The Paris-Harrington Axiom" by Ketonen which appeared early in the study of the Paris-Harrington theorem, around 1979. There is already an MO question in which a copy of this part I manuscript was successfully located, however the second part does not appear in the answer. I cannot find the second part online, and furthermore all citations to either of the manuscripts that I could find are for the first part. According to the answerer of the MO question, the part I manuscript is 27 pages, so the pdf they posted is not a merged copy of the two parts. Are the contents of the second part known?
If it cannot be found, I suspect that it may have been scrapped before completion, since in Benda's "On Strong Axioms of Induction in Set Theory and Arithmetic" there is a citation to a single "Set Theory for a Small Universe" paper which was evidently never published.