I always assumed that the way investiture manifests itself is "baked in" to the shards. WoB has confirmed as much with the comments about Hemallurgy still existing in the Harmony era. I take this to mean that, regardless of the shardholder, the very fact that Preservation and Ruin are together on a world results in Allomancy / Feruchemy / Hemallurgy.
Now what this doesn't tell us, is what would happen if a shard moved worlds permanently. If Odium left to fight Harmony in Scadrial, would a new magic type pop up or would the very nature of magic itself change to some new system bearing no resemblance to the old one?
I think you're on to something but I'm not sure the math is the reason. I think that we have three magic types on Roshar (Surgebinding, Old Magic and Voidbinding). Some people try to put these into neat little boxes (Surgebinding is Honor, Old Magic is Cultivation, Voidbinding is Odium) but it seems more likely to me that they're the inevitable byproduct of the combination of three shards.
Note: You could convince me that, when the Investiture infuses the world, it looks and feels a particular way because of the Shard but it's actual implementation gets skewed by other shards present.
So, on Roshar, we might have Surgebinding because anywhere Honor was would have something like Surgebinding. But the presence of Cultivation and Odium gives it particular twists... If Honor were to move to Scadrial, suddenly Surgebinding would be possible on Scadrial but because it would be affected by the presence of Ruin & Preservation, it would look different then Surgebinding on Roshar.
IF you're right, we've got ten types
HHH - Adhesion
OOO - Division (seems the natural fit for this)
CCC - Progression (seems logical here as well)
HHO - Gravitation
HHC - Tension (picked this because Bondsmith seem most aligned with Honor so having an HHH and an HHC makes sense)
OOC - Illumination (it brings with it a certain level of deceit
OOH -
CCO - Transformation (has some destructive attributes but generally about building things)
CCH
HCO - Transportation (There's a certain symmetry to having all three of them working together to create the surge that gets you into the other realms)
I don't know. Might hold some water. I guess we'll see. If there end up being 10 types of Old Magic (possible) and 10 types of Voidbindings (pseudo confirmed) then maybe you're on to something bigger.
