What is a good email app that won't make you link a new Gmail Account to your other Gmail accounts?

I've been using Mailbox, but unfortunately the service for that app is going to be discontinued soon. I want a separate app for my university's email, but every email app I have downloaded so far shows me my real email address that I already added to my phone (Nexus 5), and then only gives me the option to "add another account", which I presume will link my real email account to my university account.

So basically, I want an email app that works on it's own, one that will not link my school email to the email that's already on my phone. I tried many apps, but Mailbox seems to be the only one so far that does this, which I can no longer use in a couple days.