This approach relies more on theoretical mathematics than conventional physics (although in theory should work within Newtonian mechanics at least).
Take the core concept of a platformer: a 2-D model of a 3-D world, and add a fourth dimension.
You will then have a world with 4 spatial dimensions (Lets call them W, X, Y, and Z). The primary inhabitants of this world should only be able to perceive and traverse 3 dimensions (X, Y, and Z), and therefore exist on a single slice of the 4th dimension (W=0).
The 'floating' platforms actually extend into the W dimension and are anchored to structures outside of the W=0 slice. Likewise, the floating items are tethered to these structures by a weaker link; when they are picked up, this tether breaks. Large bosses likewise extend into the W dimension, and can use this to affect an appearance of flight, just like the other floating objects.
Infinitely long falls could be explained by a distortion in 3 dimensional space, whereby X=100 redirects you do a different slice of the W dimension, which loops back to X=10 (basically, think portals).
High jumping could be explained by reduced gravity.