"Intention" is both a countable and uncountable noun. The plural form of the word exists, but we never count the number of "intentions" that a person has. In other words, we *never* say "he has three intentions of doing X." It is not particularly surprising that an uncountable noun in English has a plural form. For example, water is uncountable, but we do say "waters" in the sense of "bodies of water." Just think of the famous Simon and Garfunkel song - "like a bridge over troubled waters." (Note also in modern American English, we also do say "please bring me three waters" to mean "please bring me three glasses of water.") So intention can be both uncountable and countable - in the sense that the plural form exists.

'intention' is always related to some specific act, subject or situation. If you have two different situations, then you would have two separate intentions. "His intention with Mary is to marry her. His intention for where to live is to move to Ohio." If somebody asks "What is his intention?" , it will almost always be in the context of some specific act. Left unsaid is "What is his intention (regarding <subject>). "He has come back to town. What is his intention." = What is he going to do. You could just as well ask "What ARE his INTENTIONS?" = What is he going to do (related to several possibilities).