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 (requires named view access).
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.