What do you call a language that lacks morphosyntactic alignment in any real sense at all?
My old project Naidda does not mark nouns for their roles, not by morphology and not by word order (excluding datives, for which there is a preposition). In transitive sentences, agents and patients are both agreed with by the verb, and this (plus context) is the main way they are told apart. There is a single set of fused subject-object agreement suffixes. For example, a sentence could be glossed "hit-AGR he I" and the AGR suffix is what tells which hit the other. -ai marks 3sg subject, 1st person object, so if the sentence is "hit-ai he I", he hits me. But if it's "hit-j@ he I", it's me that hits him. But if, for example, both the agent and patient are 3sg, ambiguity results and context helps determine which is doing what to the other. In the rare event even context fails, an intransitive clause can be brought in to clarify. "Hit Juan Pedro. Hit Juan." (where the intransitive subject is the agent of the former sentence)... but again, this is very rarely needed.
With intransitive verbs these suffixes don't occur and there's a different set of agreement suffixes for the single argument that bears little morphological resemblance to anything in the transitive set.
So I suppose you could call it tripartite, in the sense that S, A, and P are all dealt with separately, but really I find it a stretch to try to fit Naidda into such a mold. I prefer to analyze it as morphosyntactically unaligned.
Now, among natlangs, the system sometimes called "animacy hierarchy" is also morphosyntactically unaligned in some languages (though more often it coexists with or is part of an alignment system). But I don't know of any natural languages that fail to have either an animacy hierarchy or an alignment.