Becky,
Thanks for replying. In your scenario, when a user starts an assignment - should it still be available to other users? Do you need a record of who took what action on an assignment; for example, which user started it?
We're currently working on support Offline for Workforce Projects and that work is very much connected to a several foundational rules within the Workforce app; Workers only see assignments assigned to them. Once an assignment is started, we assume that worker is the only user changing the assignment (i.e. the Dispatcher cannot change an assignment that is In Progress).
The scenario you're outlining where, any user can start/complete an assignment, will run into issues with future versions of Workforce. Your use case and requirements are valid, but I don't know if Workforce is the app to use for solving them. It might be better to take this discussion offline into email or a call to dig into this a bit more. If you'd like to do that, please send me a DM or email the workforce4arcgis@esri.com alias and we can set something up.
Craig