As a viewer, you can request edit rights on a whole map or on a specific diagram. Click on the three dots menu of the map's right sidebar and select "request edit rights" if you want edit rights on a map generally. The map owner will receive your request as an email.
You can also request edit rights on specific diagrams in a map. To do this open map management from the diagram editor:
And select the diagram in the hierarchy that you're interested in. Select the "Edit rights" tab in the right sidebar and click "Request edit rights".
You will see a dialog which you can use to send the map manager the message justifying your request.