Upvote:1
From the Visa Waiver Program page in the section on whether you should apply for a visa instead of an ESTA:
Also, if you intend to extend your stay beyond 90 days or change your status once in the United States (for example, you intend to request change of status to student or temporary worker, etc.), then you need to apply for a visa.
Upvote:2
You are staying on a VISA waiver, not ESTA.
ESTA renewal only means updating your record in a database of people pre-checked for a simpler temporary entrance process. It's the person at the immigration counter who permitted you into the country, for 90(?) days, using data they gathered on you after ESTA registration.
Remember that ESTA registration is valid for 2 years. It's the registration for a process, not a permit. It also doesn't guarantee you will be permitted.
For longer says, you usually have to go to a consulate outside the U.S. and apply with a bunch of paperwork. So yes, you will probably have to leave, spend some time on a different continent, and re-enter. A short trip to Canada and back will also make the immigration officier suspicious. The Waiver is for occassional, short visits to the U.S. - it's okay to spend more than 90 days if it's say 10 times 2 weeks, with always a few weeks in the UK inbetween; because then it is convincing that your primary place of living is in the UK. If you have been abusing the VISA Waiver to work there, be also prepared to be rejected. There is a story on a UK (?) amateur musician being refused to enter and full body searched, because apparently he had played for tips in a bar somewhere once...
It's best to play strictly by the rules, as it is probably not fun to be questioned for hours, refused, and sent back.
So if you want to come back after your 90 days, you better apply for a real VISA, using the regular process at the consulate of your home country.