Firstly I would suggest having a hard think about whether you actually need a menu that deep and why.
Then try to think of an alternative way to structure your data to achieve what you need to do.
The reason is that this is not an easy thing to change (and 15 levels of menu suggests possible information architecture issues).
There is a drupal.org issue https://drupal.org/node/274270 relating to this that has some examples on how you can make the change.
The example is for drupal 6 but pretty much the same thing applies to drupal 7.
The problem is that each level has it's own column in the menu links table, so you have to alter the menu links database table to add new columns and then make some changes to drupal core to use these new fields.
As a side note, there is a module called menu depth limit that allows you to set a lower limit but not a higher one.