They can certainly both give them a 200pts deduction, and expell them outright. What would happen City in relations to the Nationwide would be a result of the deals in place between PL and the EFL, and wether EFL would take some separate action towards City outside of that. Given the cost and scope of the PL’s action against City, I somehow find it hard to believe the EFL would be able to do something similar.
Either way, this shouldn’t be relevant to the PL, who are not responsible for their member clubs’ dealings with other organizations like the EFL. They need to have consequences within their organization to at all stay organized.