This question is based on some new information I gained after reading up on the Chaos Damage enchantment from the Dragonborn DLC on the uesp wiki. According to the wiki, only the final effect, the Shock damage component, actually scales with Enchanting skill and perks, while the Fire and Frost Damage aspects remain at their base value, despite the fact that the description claims that all three effects are stronger with higher skill level, perks and soul gem size. You can increase the magnitude of these enchantments with other post-enchantment boosters (such as the Augment perks in Destruction, or the 3 Dragonborn DLC masks that increase Fire/Frost/Shock damage respectively), but I consider those boosts rather than actual scaling.
While I don't know of a way to confirm this for myself in-game, it seems accurate based on the only other vanilla dual-effect Enchantment, the Fiery Soul Trap effect, which only scales its Soul Trap effect and not the Fire Damage component.
So my question is is there a way in the CK to create multi-effect enchantments that can bypass this restriction, some way to "trick" the engine so to speak into seeing just one effect rather than two or three, allowing all of them to scale. The uesp claims that the engine only scales the effect with the highest base cost (Shock Damage for Chaos and Soul Trap for Fiery Soul Trap). What would happen, for example, if you altered the base costs of all the effects so that they were exactly equal?