In a nursing home, can you self pay to receive more therapy?

You should not have to pay, Medicare should pay. Sit down with the PT administrator about what more you would like to see done. Patients have physical and emotional limits; don't push too hard

You would need to check with the nursing home Admin Dept.   If yes, chances are you would need to use the physical therapy group they already have on site.

Since this is in-house, the group could try to see if some extra therapy can be given.   But don't be surprised if the group says that the therapy your Dad is getting is the limit they can give, at this point in time.   Therapy group would know best.