Install/update on computer without admin privs

We're trying to rollout the desktop app for users across our 100+ employee company.  Users are NOT admins on their computers.  We use a tool called PDQ Deploy which hasn't been able to do it.  PDQ and Wrike have been very helpful in trying to get this working for us, but we can't.  We've tried via scripts, and via GPO, but I'm missing something somewhere.  Surely there has to be a few others who've ran into this and figured a way, so just reaching out here to see if I can get any help.

I know the app has to be closed to update, and that part is easy, but since we could be running different versions of the app, we need a solution to uninstall whatever version it is, and install the version we're pushing out.  I know if we run it manually on a workstation as an admin it works fine, but we can't do it remotely.  

Thanks for your help in advance!