This might sound silly, but I was wondering if any mods exist to increase the chance of other sims calling my household to chat, invite them out for a date/outing, and the like. My sims know plenty of people and yet they are practically never on the receiving end of phone calls.

Also, does a mod exist for sims to randomly invite themselves over to the house? Like: "Hey, so-and-so, it's me. I was wondering if I could come over right now to hang out?" [Yes/No]

(If not, hmm, I might be able to take a stab at one or both of them. The second one sounds like it could be manipulated from the "Sneak Out" interaction.)

I haven't seen such a mod; first I would recommend making sure you don't have mods that are suppressing such calls, like CJ's No Random Calls, etc. Next, I'd say that if you aren't receiving too many calls, are your sims going out to community lots, especially downtown? Sims who are new to the hood or who network, or who go out on outings and dates tend to receive more phone calls.

I also don't know of a mod where sims randomly invite themselves over, though it does happen via chatting on the computer. If sims are friends, when you chat on the computer, they can ask to come over. I would look at that and maybe see if that can be incorporated/copied over into the phone chat.

Otherwise there's Sims Always Ask, Or Sims Never Ask "Can My Friend Come Too?" by joninmobile, so if you want, sims can bring others when you invite them over. And there's TS1 Prank Calls by LazyDuchess, which does increase calls, but it's pop up messages. But you could look at that, too, for your mod, as well as phonehack which makes other sims call your sims to chat when their relationship gets low, rather than just calling to give the "we haven't hung out in a while" pop up message.