How many morphemes does the word "dost" (Shakespeare) have? How many morphemes does the word "thy" have? How many morphemes does the word "thou" have? Are "and", "if", "of", "a", "but", and "in" considered morphemes?
Thy is a reduced form of thine, which is the genitive of thou. It could therefore be argued that thine, at least, consists of two morphemes, thou and its inflectional ending. Whether such an analysis extends to thy would no doubt serve to keep grammarians amused on many a long winter evening.
And, if, of, a, but and in are all morphemes.