How about having a special badge having acquired 10, 25, 50, etc. badges?
I would have to count the exact number of badges I have acquired so far, but it might be close to 50. I guess there are several other people who are in a similar situation and who may find it difficult to choose something appropriate for "Me in 3" in the account profile.
Someone may have accomplished 5 mission badges in database and systems, and 5 mission badges for being correct and helpful, which could give the user a special mission badge for having accomplished 10 mission badges. The next one would be given at 25 for which the user needs 5 more, and so on. These badges could then be used in "Me in 3".