Different arts have different ways of promotion. Most arts don't get to 10th degree, some do. For some arts, 10th means you have reached full transmission of the art.
Now to the guy who posted above me. You clearly do not understand the Taijutsu (ninjutsu) ranking system. 11th-15th dan in the art is still actually 10th degree, just at a different training priority in training. In order to understand it, forget everything you know about the typical japanese dan grade.
For starters, there is just 3 belt colors. Mukyu (10th kyu) is white, meaning you have no or slight training. 9th-1st kyu is green meaning you are LEARNING the basics. Shodan (1st dan) is where you have grasped the fundamentals of the basics and actually can start moving on with the real training (much like the shodan of any other art). Now here is where it gets tricky. You can start being an assistant instructor at 3rd (sometimes 2nd if sponsored). You are not considered an instructor until Godan (5th degree). You are a master instructor at 10th, but each step after that (11th-15th) correlates to a different level of understanding and teaching. You may find this odd, but the way the belt system is structured actually correspond to the old way that the schools in the system were taught (shoden, chuden, and okuden).
Shoden (not the shodan belt rank but basically means lower levels) comprises the 1-5 dans
Chuden (mid levels) is the 6-10 dans
Okuden (upper levels) is 11-15 dans..
Unlike other martial arts, you aren't considered a shihan until 10th dan, and you can't even begin to hope for Menkyo Kaiden until 15th dan.
So to answer your question, EVERY art is different, and some don;t have 10th degrees. Some have different levels of 10th degree (as I stated above). Only by being promoted by the headmaster or someone higher than you can you ever move up (unless you become the headmaster, in which most either stop claiming a belt level or stop at the highest level they have achieved).
EDIT: forgot two things, 1) a shodan in any art means they have a committment to that art and are good at the fundamentals. 2) somewhere after shodan you quit caring about rank and start caring more about skill.