"Big Sister"... Maybe a 5th or 6th grade girl who would be willing to spend a recess now and then hanging out with DD and any other "single" kids. Has anyone ever done this before, and was it helpful at all?
On an individual basis, I'm aware of one school considering a buddy plan to welcome a student who was grade-skipping but after discussion and prior to implementing the idea, the school decided against it as being a burden for an individual student. I agree.
Some schools have a "big buddy" program in which all kiddos in a higher grade are matched with kiddos in a younger grade. When the numbers don't work out perfectly, a few kiddos may be a big buddy to several younger kids, or a few duos of big buddies may mentor a younger kid. In this way, no one is singled out. Buddy-day may be once a week or once a month. Schools may have occasional pen-pal days on which each kid writes something they like about their buddy(ies), then the letters are delivered to the buddy(ies). Kids may be given a "theme", open-ended "thought question", or "conversation starter" as ice-breaker on each designated buddy day... for example "what is one thing you would change about school..." etc. Big buddies may be assigned to walk with their little buddies to school assemblies, etc, keeping lines moving smoothly through the halls and providing a big help to teachers. Kids seem to look forward to seeing their buddy(ies) and the buddy plan seems to promote understanding and a sense of every student being important and making a difference.