Some questions have tricky answers, but not this one. The answer is NO.
A theorem (Earnshaw's theorem) shows that any collection of static
classical objects interacting via electricity, magnetism, and gravity
will not be in stable equilibrium.That means none of them will be
stably supported out of contact with the others. That applies even if
you use many objects, not just three.
You can get stable equilibria if non-classical quantum effects
are important. These become important whenever objects are in contact,
so Earnshaw did not prove that you can't build a house. They can also
cause another non-classical effect, diamagnetism, in which objects
actually are repelled from strong magnetic fields. This becomes a
strong effect for superconductors, which are often used for little
Another way to escape the conclusions of Earnshaw's theorem is to
allow the magnets to be non-static. One example of levitation not using
a superconductor is to make a many-turn loop of wire with an
alternating current in it. This object will float above a conducting
metallic plate for a similar reason to why a magnet will float above a
superconductor -- currents flowing in the plate will create magnetic
fields which oppose the external one applied from the loop of wire.
These will eventually die away resistively for ordinary metals (but not
superconductors), and so the oscillating magnetic field is necessary to
keep the coil levitated.
You can also arrange stable levitation with a feedback mechanism,
which rearranges the magnets or redirects current through
electromagnets so that when the levitated object begins to slip and
fall, the fields are changed to push it back up again. Some
magnetically levitated train designs rely on this kind of mechanism to
keep the train properly levitated with respect to the rails at all
(published on 10/22/2007)