Looking in the other direction, our solar system orbits about the Milky Way, the Milky Way orbits with other galaxies that comprise the Local Group. The Local Group is a part of the Virgo Supercluster, but now we're getting so big that the expansion of space dominates over gravity. The point at which the expansion of space dominates over gravity places a limit on big side of the picture regarding how large the gravitational hierarchy can get.
If everything was a point mass, then mathematically one could (I think) come up with an infinitely deep hierarchy. The reason I said "I think" is that the N-body problem doesn't have a nice analytic solution. While a solution to the 3-body problem does exist, it is not in the elementary functions, and it has some nasty collision and escape special cases. The 4-body problem is even hairier. Beyond that, except for some specially constructed solutions, the N-body problem is pretty much intractable.
Looking away from abstract mathematics and toward the physical world, it is quite possible for a pair of stars to be orbiting one another at a close distance. Planets can orbit about the binary pair and satellites can orbit about these planets. So in a sense this is third order hierarchy. It is also possible to have a binary pair that are orbiting at some distance from one another, with each star in the pair having its own planetary system and the planets having satellites. So yet another third order hierarchy. Similarly, a pair of similarly-sized planets could be orbiting one another and have satellites orbiting about them. Combining this with the binary star would yield a four-level hierarchy.
However, I don't think that this four level hierarchy is quite what you are looking for. Restricting things to a strict hierarchy where the masses on a given level are orders of magnitude smaller than the parent level and are not co-orbiting other objects on the same level (no double stars, no double planets), the answer to your question is "probably not".
One problem is dynamic stability. Physical objects are not point masses. There is no way a body (call it X) orbiting some larger object can have sub-bodies in stable orbits about it if X's Hill sphere of lies inside X. For example, the Hill sphere of the International Space Station has a radius of about a meter. The ISS cannot have satellites.
By this measure, the Earth's moon could conceivably have satellites; the Earth-Moon L1 point is about 60,000 km from the center of the Moon. Now we have another dynamic problem.
Huge objects such as the Sun and Jupiter are extremely close to being oblate spheroids. The Earth is fairly close to being an oblate spheroid, but departures from this do exist and do have an effect on orbits. This departure is why geostationary satellites are attracted drift toward 75.3°E or 104.7°W longitude. Smaller objects such as the Moon are noticeably lumpy with regard to gravity. Even smaller just objects don't have enough mass to pull themselves into a spherical shape. Low lunar orbits are not stable because of the Moon's lumpiness. An interesting read on a pair of objects released into lunar orbit by the Apollo program:
http://science.nasa.gov/science-news/science-at-nasa/2006/06nov_loworbit/.
So, for a moon of a planet to have a satellite,
- The moon has to be quite far from the planet so as to have a reasonably sized Hill sphere,
- The moon also has to be relatively massive so as to have a reasonably sized Hill sphere,
- The hypothetical satellite's orbit has to be well inside the moon's Hill sphere, but
- The satellite's orbit can't be so small as to allow the moon's gravity anomalies to do some very weird things to the satellite's orbit.
That's a pretty narrow window. Now the question arises: How does the satellite get into that window? Some of the giant planets have moons that formed with the planet. Those giant planets are so big that they developed their own accretion disks as they formed. The moons of smaller planets such as the Earth's moon most likely did not form this way; those smaller planets are just too small for them to have had a substantial accretion disk. Satellites of planets are far too small. This route toward a moon having a satellite just doesn't exist.
The other mechanism is via capture. One way to capture a satellite is to collide with something; this is the most widely accepted hypothesis toward the formation of the Earth's moon. Another is for conditions to be
just right so that a some incoming body on what appears to be a hyperbolic trajectory transfers angular momentum to the central planet and becomes a satellite. These windows are very, very small.
Bottom line: The odds are pretty much against a moon having moons.
