I saw you had a lot; I had assumed you had bred them. I actually looked at them just now, and except for the hidden one I can't see, they are all "stolen". Hmmmm. How'd you do that?
Is it possible that you got some that were abandoned? Maybe abandoned eggs/hatchlings don't count as part of the limit of 4?
I just went through several of the people on this thread who have more than 4 eggs/hatchlings. Some are like me, they got an extra one because they bred it. Others have 5 or more "stolen" eggs. Epona142 and AshleyB are the ones that I noticed. So guys how'd you get more than 4? Share your secrets!