It might be freaky but how about having all your alts in a home instance as NPCs. Even better if in your (if we had) guild hall, everybody’s alts were there as NPCs? This would introduce the party feel you get in other MMOs where you could just stand around and chat, without it just being an empty lonely room.
Maybe even a fight simulator where the alts would battle each other now and again, have guild scoreboards? Aka championship manager for alts :p you could check back every day to pick up your winnings (everybody loves a time gate, right?), bet on people’s alts, alt podiums!!