For the free accounts - from what I have seen, there isn't a way to add collaborators (unless that changed recently).
If working in an organization account, you have to add outside emails to the organization before they can collaborate with editing. I would contact the institution and see if they can add you to their system, and then you would be able to collaborate.
Side note - theoretically, you could create one account depending on the organization's security settings. If it's Google login it won't work for the most part (rare occasions it will). However, multiple people can't edit the same project at the same time, even on the same account, so that's something to keep in mind! It will either lock out or override edits.
