Here is what I was describing above, but presented instead as a visual.
The current BG3 party comps using a sample set of 3 (ie. party of 4: Player +3 other characters.) I arranged them in order of likely recruitment, although the first 4 companions can be recruited in whatever order, but just going off the path of least resistance something like so...
![[Linked Image from i.ibb.co]](https://i.ibb.co/0MLr9tT/Badlurs-Gate-3-party-comp.png)
I wish I had the energy to do the same for the party of 5 (sample set of 4, or the player +4 others), but it gives an impression at least. Also helps probably to suggest which party comps are less likely owing to the requitement sequence. Characters that we meet later on, this is reflected in the likeliest comps just going down the columns and rows.
Also, here's something fun...
It shows the character portraits for pretty much everyone in the game. There are 1,634 total thus far on the wiki, broken down in pages of 200 portraits, arranged alphabetically by character name.
*spoilers*
https://bg3.wiki/w/index.php?title=Category:Character_Portraits
As the pool of recruitable companions climbs it's basically a 'grains of rice on the chess board' scenario. The number of potential Party Composition combinations starts increasing to the point where it's really not even possible to fathom anymore, cause the numbers are so large. The pool of recruitable companions is more important than the party size for that, but at the low end party size also makes a pretty significant difference. The closer it is to the split, the higher the number of potential combinations without repetition.
Not that one needs that many. Just imagining what it would look like if one were to say, add an Alfira, or a Viconia, or a Sarevok the numbers climb quickly even with just a couple additions there.