The maximum length of a Disney ticket really is 10 days. You cannot extend your park pass after that. If you want to spend more than 10 days at WDW, you have three possible options:
- Buy a 10-day ticket, and then buy a separate 3-day ticket. The disadvantage of this is that with your second ticket you'll have to start back at the full ticket pricing.
- Buy a 10-day ticket with the Water Park Fun & More add-on. This gives you 10 days in the theme parks and 10 admissions to the water parks or DisneyQuest. If you're expecting to use the water parks a lot or spending time exploring the resorts, you may not need more than 10 theme park days. You can read more about the WPF&M option
HERE and
HERE.
- Buy an annual pass. Many guests find that once they're spending more than 10 days at WDW, it make sense to have an annual pass. In addition to getting you into the parks for an entire year, the annual pass also has other benefits such as discounts on some shops, restaurants, and tours, as well as occasional room discounts. Another perk of the annual pass is that it allows you to purchase the Tables in Wonderland card. You can read about this
HERE,
HERE,
and HERE. I am a HUGE fan of the TiW card. To me, that makes my annual pass purchase completely worthwhile.
Enjoy your extended stay at WDW!