Is it a bolt on neck?
If so then do it seperatley, othewise I'd do them both at once. If there are no neck join issues to be fixed.
Pics always help with advice.
Just a thought, if its a Gibson or guitar of value, the damage your doing to its resale maybe substantial. Your guitar and your decision but at least research that. I know when I have time that I can afford to have it down by black studio will become lockness green.