V2 is a peculiar syntactical structure present in western and northern Europe, which governs where the finite verb goes in a main clause. Historically, it has had some presence in some Romance and Celtic languages, is still present in almost all Germanic languages, Estonian, and is also present in a few other languages worldwide. There's differences in whether these languages apply V2 to subclauses or not, (or even to what types of subclauses they apply them), and how strictly the V2 rule operates.
When trying to come up with new ideas, I like to 'parametrize' a concept and alter the parameters.
The first parameter of V2 that occurs to people tend to be the number, and of course, increasing that to 3 is an obvious idea. And naturally, one could even go further, to 'V4' or whatever, but such seems to require increased numbers of mandatory arguments, dummy arguments, or permitting V3 and V2 in circumstances where too few arguments are present.
However, there's a few other things we can do. Besides, grammar in general seems to be bad at counting past two. However, it seems to be rather good at counting both backwards and forwards. Thus, we could have V-2, where '-' denotes minus, and I'll parse that as in python list comprehension - i.e. counting from the end. This could signify having the verb always being the penultimate word.
This could lead to VS but SVO, but also SVAdv, etc.
However, there's a different parameter we can change: S2 - subject second! VSO, but also permitting OSV, AdvSV, VSAdv, etc. O2 is of course also conceivable, (or erg2 or abs2 or whatever), but in the case of O2 or Erg2, we do run into the question of how to deal with intransitive clauses.
We could also have a more general NP2, where any noun phrase qualifies. One could imagine having a subset of possible arguments: (S or O)2, or even weirder pairings like (Adv or V)2.
In Swedish, there's a handful of adverbials that can go between the subject and the verb, or at the beginning of a clause yet be followed by SV. Such lexical exceptions can of course also be considered for a conlang.
A different parameter we could imagine changing 'where does the rule apply'. For now, V2 applies on sentence level. We could imagine a similar rule that applies in a verb phrase or in a noun phrase, e.g. 'article comes second' or 'TAM marker is the second constituent of the verb phrase'. I am aware of some such rules in some languages, esp. w.r.t. articles and e.g. Wackernagel-position clitics in Latin and Russian.