The maximum level for any base class is 20. However, it is possible to go beyond this into the epic levels.
Now I wonder; Is the same essentially true for prestige classes? Take for example the Mystic Theurge, which ends at its 10th lvl. Is it possible to take an 11th, 12th, etc. lvl of this class in order to keep progressing an arcane AND divine spell list?
You can advance some prestige classes beyond their normal level limit with epic level progression. However, you can only do so once you're already level 20 with non-epic classes. As the epic rules describe:
A ten-level prestige class can progress beyond 10th level, but only if the character level is already 20th or higher.
There is an epic progression available for the Mystic Theurge, but it alternates between arcane and divine spellcasting progression every level rather than advancing both, so you'd probably be better off just alternating levels in your original classes - you'll get the same spellcasting and whatever other normal class features they have.
Prestige classes that don't have a full ten-level non-epic progression don't get epic progressions later.
The Mystic Theurge can take levels beyond 10 once the character reaches epic, since there is an epic progression for it. Note that it only progresses spellcasting as if you were alternating levels between an arcane and divine spellcaster, so it isn't actually useful at all.
In general, prestige classes with a published epic progression can take levels beyond what's listed in the class. There aren't a lot of these, though. For other prestige classes, you can ask your DM to come up with or approve an epic progression, but it's up to them. You may also want to do this for the Mystic Theurge, since its published epic progression is so terrible.
...and the expanded epic rules found in the Epic Level Handbook both support the progression of full 10 level prestige classes into epic levels.
The original epic rules, however, give no examples of how to progress prestige classes, only guidelines.
For example, in the original epic rules, it only mentions that prestige class features that user character level as part of a formula to calculate a save DC progress at half character level after 20th, (the example used is the assassin death attack) and that class features that progress in a steady pattern also continue to progress (rogue sneak attack or barbarian rage) , but not ones that come to a stop before 20 (monk's damage) , or ones that are granted once (fast movement).
The DMG guidance listed may result in different effects when applied to prestige classes. For example, the Mystic Theurge will continue to gain both divine and arcane level boosts every level according to the DMG epic rules, which are primary source, as opposed to the SRD rules.
