Live Chat with multiple logins

I have been researching live chat plugins, which has caused some confusion because I am not sure which is appropriate for:

I have created a website which links schools. I want to use a live chat between the schools that are linked so they log in with their school name.

Also I want separate live chats for different school links as I have 40 links in the website.

I thank you for any help you can give me on this.