The H-1B can continue to be extended, in one-year increments beyond the 6-year maximum, provided a labor certification has been filed on your behalf. As for going to another employer, that is also possible, but the process of the labor certification has to be restarted with each new employer as the labor certification application IS employer and location specific.
Please let me know if you have any additional questions or if I may be of assistance to you in this matter.