Lots of ideas for that...
- I suppose the two characters in the front would make the most sense for the two open menus.
- "Charge": This could do a number of things. Maybe the party lunges a whole tile forward and attacks the enemy immediately, like a super-fast attack made by either all characters or just the ones in the front row. This attack could also deal extra damage. As a downside, the party could be immobilized for a few moments after that, so it would be a powerful, but risky attack. A variant would be an option that simply lets everyone attack, like the "all attack" button in EOB3.
Those two options would apply to all party members. Keeping with the theme of an attack option only applying to the character that uses it, "Charge" could be just a powerful, but risky and exhausting attack that deals lots of damage, but has a long cooldown and a rather low chance of hitting the enemy. But this would make it just another attack option like all the others...
Beware: the concepts I wrote about above are very hard to balance, I suppose...
- "Bargain": This could do all kinds of stuff involving interaction with monsters or other dungeon inhabitants, but this would be very hard to incorporate into the current engine. I suppose it could be an option similar to War Cry, but rather than fleeing from the party if the attack is successful, the monster would just wander around randomly unless attacked. The rate of success should depend on the monster's type (Trollins, maybe even Screamers would be more likely to get affected than, say, Skeletons or Deth Knights) and some attribute of the character - maybe his/her priest level?
- Friendly and Hostile: I'm with the other users here, if you treat a character badly (lots of injuries, no food or sleep), he gets hostile and eventually leaves.
- Feasting and Fasting: Probably just food.
- Relaxed or Wary: This could mean two things for me (probably because of my bad English

):
1. Fresh and Tired: If a character doesn't get enough sleep, he gets tired. This could mean that his/her attacks are more likely to miss, that the cooldown after his attacks takes longer, and maybe that spells even require more mana. The interesting part about this is that sleep would actually matter in a new way. Currently, sleeping is just speeding up the natural recovery. This way, sleeping would be an actual gameplay element.
2. Calm and Nervous: I think this would be even more interesting than option 1. If a character is nervous, his attacks could also miss more often, he could be more likely to fizzle a spell, or he would even do random things like turning around in the heat of battle or attacking thin air if a monster is nearby, but not directly in front of the party, resulting in an annoying cooldown when you actually face a monster. In order to become more calm, the character might need sleep and some special food. Apart from the nutrition value that food currently holds, each food type could be given a second attribute, the "calmness-level", so to speak. Maybe Screamer Slices are sort of drugged and add a lot to the calmness. Or the vitamines in an apple add to the calmness. On the other side of the spectrum, drumsticks and dragon steaks could (should?) add little to the calmness level. This makes different types of food interesting for different reasons. There could also be a new "calmness potion" as a priest spell, but this should be made extremely hard to cast (similar to VI in Conflux maybe).
Just a bunch of random ideas, maybe there's is something among it that warrants further discussion.