Just following up on this old thread for anyone following.

We don't have this feature but if anyone wants to build it the Save & Copy plugin would a good place to start: 
https://www.interactivetools.com/plugins/save-and-copy/

It saves the record and starts with a new one.  So the difference would be saving the record and then redirecting to the next record to edit.  You'd want to consider the user's current sort order though as that would affect what was considered as the next record.

Let me know if you want to revisit this in the future.

Is it feasible to add another button next to Save, Erase and Cancel when viewing a detail record.

'Save and Go To Next Record' would save the current record, and the open the next record number in the list.

Unfortunately I don't have any budget to take it to support. 

Cheers