I think there's going to have to be some second level of "alignment" to get distinctions within each "bucket." I agree with the general groupings posited above (Personally I'm calling them: Exist, Change, Bind, Proceed). One obvious option would be if each Shard has a "primary" and then in each bucket one would be "pure" and the other 3 would each pair with one of the other Commands. I've started trying to organize it by this but haven't come up with groupings I'm fully satisfied with. Preservation as "Exist Proceed" (or "Proceed Exist") and Ruin as "Change Bind" makes an interesting complement, though: Preservation has the goal and the sustenance, but needs the raw power of Change that Ruin provides. Hemalurgy also makes sense as a Connection-oriented power, at least to me.
My other completely half-baked aluminum-hat theory comes because I noticed some of them feel like they're *three* of the Commands (Cultivation is definitely Exist and Proceed, but it feels like Change belongs in there too. If we look at the combinatorics, there are exactly 16 ways to combine 4 items if order doesn't matter:
4 singletons
6 doubles
4 triples
1 All 4
1 None
If we take the theory that The Shattering was from using all 4 Pure Commands on Adonalsium itself, then I could see "fractures into all possible combinations" as a reasonable response? I haven't found a layout of the Shards I'm happy with, but am definitely poking around some. One thing I'm toying with is whether or not having Proceed somehow maps to futuresight? I'm not super satisfied with this model, but I at least want to kick the tires some now that we have all the names, bearing in mind that there's definitely a layer of human interpretation at work....