Theoretically yes, sure, at least to the extent that you're not exceeding the lifting capability of any of the devices (presumably you're mostly limited by the bottom one, or you'll need to make ones that get ever smaller as they progress upward).
Practically oh, my, that's going to be a challenge.
First, yes, you can have wires connecting the floating bits -- why not? It may be a good idea to have some sort of a cage that restrains how much they can move, so that in the event of power loss or other failure the bits don't jump around and either break themselves or get lost. You'll want to source really flexible wire, and if your first try lives long enough to break from wire fatigue, you'll want to get some wire that's made for continuous flexing (it's out there). Buy that wire new, or harvest it out of some device that already has it, like a printer.
Second, you'll need to make sure that your base has enough raw lifting power to lift the higher-up bits.
Third, and the biggest part of the challenge, is that the various bits will interact. Getting the first part working, where you're just floating a magnet in the air with a dead load on it, will be a challenge. Then you'll need to replace that dead load with a load that's not only live, but is responsive to how it's base pushes on it.
Think about this -- if you hold that floating apple gizmo in your hand, and lift your hand suddenly, it'll push back, but it'll do so after a bit of a delay. That's the load that the base will see when you put the second layer onto your assembly.
I can almost guarantee that if you just design two independent levitators, get them tuned up, then try floating the second stage on the first, that the assembly will be dynamically unstable. This effort will either take a whole lot of messing around to work right, or it'll take some advanced control techniques (I'd start by modeling the whole mess in state-space), or possibly both.
Image from the same source as the video link.
