Up to 384 minor planets (including Pluto) qualify as planets? In 2006, the International Astronomical Union redefined the definition of planet in order to exclude Pluto, Eris, and several other objects whose category was disputed. This new definition of a planet featured 3 criteria:


A planet must be massive enough to achieve hydrostatic equilibrum and
become ellipsoidal. 
A planet must orbit a star or brown dwarf (with the exception of planemo).
A planet must be massive enough to clear any nearby objects.


Pluto and the other objects apparently failed to meet the 3rd criteria, as they had not cleared the nearby Kuiper belt objects, so they were reclassified under the term "dwarf planets".

But what if Pluto actually has met the third criteria? It's probably well-known by now that Pluto has 5 moons. The largest moon Charon is over half the size of  Pluto, and is frequently classed as a dwarf planet in its own right. The other 4 minor moons Nix, Styx, Hydra, and Kerberos, are much smaller then Charon, and are similar to the many asteroid-like moons found around gas planets. 

The leading theory for how these smaller moons formed is that they are leftover debris from a collision between Pluto and another object, but it's just as likely that they were Kuiper belt objects that were captured by Pluto (just like the moons of Jupiter and Saturn). If they were captured, this means that Pluto has technically cleared 4 objects from its neighborhood, and so it meets the 3rd criteria. 

The same logic can be applied to Eris, 2007 OR10, and the 400 other dwarf planets known to host moons. So should we have 392 planets, keep the current definition, or scrap or redefine the term "planet" entirely?
That actual IAU Resolution B5 adopted at the IAU General Assembly in 2006 states:

(1) A planet is a celestial body that:
(a) is in orbit around the Sun,
(b) has sufficient mass for its self-gravity to overcome rigid body forces so that it   assumes a hydrostatic equilibrium (nearly round) shape, and
(c) has cleared the neighbourhood around its orbit.

The last part being the neighbourhood around its (whole) orbit is the important part; it's not enough for Pluto to dominate its family of moons (and this last part is debatable as Pluto and Charon orbit a common barycenter (center of mass) which is between Pluto and Charon since Charon is so massive, compared to Pluto).
Since Pluto orbits in the Trans-Neptunian region with a similar orbit to other bodies, some of which are similar or larger in size and mass (Eris), and cross the orbit of Neptune, it can't really be said have to &quot;cleared the neighbourhood around its orbit&quot;. Indeed Pluto is the prototype of the Plutinos; object which have a 3:2 mean motion resonance with Neptune (orbiting twice for every three orbits Neptune makes).