@Auro: This is a collaboration of different people and it will have different styles, but, to make it polished, it would be best for everything to be based off a simple premise and have common elements. Having the stories unorganized would distract from the quality, as I have said before. The creativity is in your unique pet-tan story.
If one person has the little sister and another person has Bob the veterinarian, when players play through other parts of the game they may ask "Wait, so the MC's little sister doesn't exist in (insert pet-tan's name here)'s world?" Good games don't make players question the writing.
It's a collaboration of talents surrounding a main premise, everyone adds their own unique pet-tan to the world, but they shouldn't change the world. Everyone's already showing their unique stories and perspective through the pet, and since there are a lot more people getting into this project, each story should only focus on the pet-tan for simplicity's sake.
Also, for writers, I've found some good inspiration for writing about your pet (though you might already have done it) Research guides on how to take care of them! Guides like that can help you develop funny situations for your pets. For example Ferret-tan eats a lot, like real ferrets in real life, so the MC runs out of food!
Here's a good guide for you, LVUER: http://kerryg.hubpages.com/hub/praying-mantis-care

