Does "so that" function as a conjunction together

He cleaned the dishes [so that he had clean plates].

Although "so + that" may appear to be a single grammatical unit, i.e. a conjunction, it is best analysed as two distinct elements: the preposition "so" + the subordinator "that" introducing the subordinate clause "that he had clean plates" functioning as complement of "so".

The whole expression "so that he had clean plates" is thus a preposition phrase functioning as an adjunct of purpose (or possibly result).