I know this isn't game-breaking or anything and she's still clearly trash (...for now), but I thought you guys might find it interesting.

I've been using Solomon with my mostly Wind Element team (Gaia/Shiva/Hermes/Nike), and noticed that with her skill "Solomon Ring" which does an attack in each element, the elemental damage is affected by the Eidolon(s) you have equipped. For example, when I'm just doing an Anzu run and thus have no "[Element] Attack +40%" effect, the damage is about 1500 per each element's attack with a slight decrease for the opponent's strong element and increase for the opponent's weak element. But when I have a particular element's Eidolon equipped, say with "Water ATK +40%", no matter what element I have equipped to Solomon her Solomon's Ring skill damage goes up during the part of the skill where she casts that element.

Why is this interesting? Because several Eidolons, like Behemoth (+30% to Wind/Water/Light) or Takemikazuchi (+30% to Wind/Thunder/Dark) increase multiple attributes at once. And during Solomon's ring, ALL of those elements are buffed as well.

It's still early days so I haven't taken the time to spreadsheet up how much different that is than just a straight single element increase on a single element skill, or written up a 10 page treatise on how this totally makes her OP. But it's a neat effect and I figured since very few people play Solomon they might not be aware of it.