Hi,
Your regular Customer Service staff won't need the full Plan 1 license. They can have the Dynamics 365 for Customer Service Enterprise license.
Now for the other users. When you would want them to update the case - even only the resolution field - they would need the same license. This is since updating the Case entity would require the Dynamics 365 for Customer Service Enterprise license.
There is a workaround you can do which works fine. There are Team Member licenses. These are affordable (about $ 10,- a month for a user). Users with this license are able to use the Activities. When they need to act regarding a Case, you could send them an activitie that they need to update. When they update the activity with the resolution you can use a workflow / flow to update the Case with this resolution and you're all set.