The only way I can think of doing it is the old ceiling pulley solution (like a kitchen airer, eg http://www.ecowashinglines.co.uk/product/CIS-DKM) that people use to stash their model railways.
Base level sits on existing table/trestles & is the dungeon/cavern. The built up walls of the area are of an even height so that the next level can sit cleanly on top.
Next level rests atop the base dungeon & is roped up so that it can be raised out of the way or just a couple of feet. Probably find that players need to stand to access it but seated can still access lower level. (Rigid vertical guides required on 2 corners to prevent swinging?).
If this isn\'t all too ambitious pop a 3rd \"ground\" level table on top, which is presumably where the adventure will begin. You could always have lift off hills from this top section that reveal chambers beneath for when the action has half the group entering a dungeon & half cowering behind a hedge on the surface.
I\'ve seen an adventure run using a stack of 3x3 polystyrene squares (washing machine top & bottom packaging I reckon, as I have some at home!) that had been roughed into dungeon layouts. Each time the party goes down a staircase you remove a layer to reveal the next stage. Cardboard sheets placed over top to obscure special rooms you want to keep as a surprise. Good fun but a huge amount of prep time for a single game, perhaps someone who runs tournament games could justify the effort.
Good luck, B.