The "calm down" and "cheer up" socials are cute, but they seem a little heartless when you don't even know what's going on with the other person in the first place. How about a social where one can ask about the cause of a sim's mood? "Why are you feeling sad?" "Why are you feeling playful?" "Why are you feeling uncomfortable?" etc.

The sim could then respond with something drawn from one or more of their moodlets. Maybe the moodlet's hovertext in a notification, or maybe the picture from the moodlet in a speech bubble.

If a sim has just arrived on the lot in a random mood without anything in-game happening to them to cause that random mood, they could respond "I don't know, I just seem to be in a random mood today" or with the yellow question mark in a speech bubble. But sims already can arrive on the lot with a mood generated by game events, like friends of someone who recently died always arriving Sad, or people in a Juiced neighborhood always arriving Dazed, and those could respond with the tombstone image or drink image in a speech bubble.

The social might not be available until the green bar is high enough. Or a low green bar, or perhaps certain traits like loner or hothead, could give a chance of the social failing and detracting from the relationship-- they don't want to tell you what's going on with them and maybe they're even angry that you asked.

(I haven't much used the "Ask what ___'s problem is" angry social, but I seem to recall it has a behavior sort of like this?)