(This question is closely related to Can I broaden the scope of a claim w.r.t. prior art through the use of "other than"?, in which I ask about patentability in case I have to compress all claims into a single independent claim.)
Let's assume there is a patent on a machine that "dries hair with hot air", and I have five other ideas how to dry hair (ice cubes, friction, whatever). I would like to avoid having to file five patents.
Obviously, I cannot claim a machine that "dries hair" any more.
When not restricting myself to one independent claim (e.g., at the USPTO), I would like to have a patent about machines that "dry hair by other means than hot air", with several independent claims claiming 1. a machines that "dries hair with ice cubes", 2. a machine that "dries hair with friction", etc. This seems possible from a point of view of writing the claims and filing the patent from a purely logistical standpoint.
However, would that still be a "unity invention"?