If you give them these privileges:
Configuration Components - Configuration - Designers - Maintain Personal Dashboard
Configuration Components - Configuration - Designers - Personalise Dashboard
But don't give them:
Configuration Components - Configuration - Designers - Maintain System Dashboard
then they will be able to "Make this dashboard my personal homepage" and then drag the dashboard gadgets around where they want them or rearrange the columns in query gadgets for example.
Does this give you what you were after or was there further customisation access that you wanted to give?
I tried this and it doesn't work. I tried to add an additional column to the dashboard and it doesn't stay.
Yes it looks like you are correct. You are able to drag around the gadgets on the personal copy of the dashboard but are unable to modify components without having the Maintain System Dashboard privilege. Could you please raise this as a support case?
Support asked me to create an enhancement:
The current setting only allows the movement of the gadget or add columns to the dashboard which isn't that useful.