I was the one who started the June (May's sister) thread jm. By all means add to it or use her somewhere else. I'm certainly not up to writing a whole thread myself like you did (great work by the way) and I don't claim any ownership just because I wrote the first chapter.
Imo one of the best things about these type of stories is that people can just chip in a chapter wherever they want as and when they have the time and inclination.