Is it possible to fly VFR above the IMC floor or VFR-On-Top without a specifically filed route, both using an IFR flight plan to go through IMC?
This question probably covers some of your points but here's some more information. See the AIM 5-5-13 and ATC Orders 7-3-1 for more details.

Can I get an IFR clearance for an area and operate there VFR-on-top?

Yes. VFR-on-top by itself is only a clearance to use VFR altitudes, it isn't a clearance to deviate from your course. But ATC can clear any IFR flight to operate within an arbitrary, defined area (ATC Orders 4-4-1):


  EXAMPLE−
  1. “Cleared to fly east of Allentown VORTAC between the zero four five and the one three five radials within four zero mile radius.”
  2. “Cleared to fly east of Crystal Lake radio beacon between the two two five and the three one five courses to Crystal Lake within three
  zero mile radius.”
  3. “Cleared to fly northeast quadrant of Philipsburg VORTAC within four zero mile radius.”


Same as above, but foregoing the VFR-on-top and accomplishing it purely as IFR.

I don't know exactly what you mean here: VFR-on-top is an IFR clearance. If you're asking how to change altitude as needed under IFR without using VFR-on-top, you can request a block altitude clearance.

Can I file two flight plans?

What would the departure point be for your second flight plan? I suppose it might happen if you departed IFR, requested climb to VFR-on-top, cancelled IFR in VMC, then called back for a pop-up IFR clearance to shoot an approach. But I don't see the point: why not just work with ATC in the first place and stay in contact with them for the whole flight?

All in all, the simplest thing here is just to ask ATC for what you need. Except in very busy terminal areas, they're very good at accommodating pilot requests, whether VFR or IFR.