Are there any languages some of whose verbs require more than three arguments? I was thinking of causative constructions, such that "Mike had John give Sally the ring" could be expressed with one clause.
I have heard the term "tritransitive" for verbs that are said to take four arguments. One example in English is this
She(1) bet me(2) ten euros(3) that they won't show up(4). As you can see, this is different from your example with causatives, because the fourth argument taken by the main verb
bet is the whole that-clause. If I recall correctly, causative constructions have been analyzed as having only two or exactly three arguments. A problem for the analysis of any construction with regard to argument structure is to determine whether two or more arguments are taken by the same predicate, and thus are coarguments. You need syntactic and semantic evidence to prove that a verb can have four arguments, and as far as I know, causatives are not part of that kind of verbs. I'm sorry I can't tell you anything else about argument structure outside Germanic and Romance linguistics.