The multi loops with a common feed should act just like dipoles do, except with higher impedances at resonance. IOW, the reactances will go up when the particular loops aren't resonant.
Now, as to parasitic radiators, it is the spacing that would mess up that idea, since different wavelength spacings would be necessary for each loop.
Here's a thought. How about an all-band "loop screwdriver?" Four support points being long springs with pulleys on each. Route the loop wire through the pulleys around to a small bi-directional winch at the feedpoint. The winch would pull in or pay out wire, thus shrinking or expanding the loop. Insulators added to keep the loop floating.