One framework I found incredibly useful when working on a multi user system is the jobs to be done framework. In fact, it's to the point where I'm a little obsessed and I have to wonder if I don't just like saying it a lot!
Basically, as well as using personas to design empathetically, the starting point is focussing on how the users will actually do the tasks they need to do. I find combining the JTBD framework for the service design with the persona driven design for the lower level design elements really helpful.
It bears repeating, the JTBD framework is not the be all and end all. It doesn't always work so you'll need to experiment how you combine methodologies which probably means taking care with the analysis. However, as I said, I found it very useful when considering how to design for multiple personas/users.
Some interesting links: