ESTAs and VWP are not the same thing, I invite to [read up](http://travel.stackexchange.com/questions/66243/what-is-the-us-visa-waiver-program-and-what-is-an-esta) more on that. 

Since ESTAs are generally valid for [2 years](https://www.cbp.gov/travel/international-visitors/frequently-asked-questions-about-visa-waiver-program-vwp-and-electronic-system-travel) and they only need to be valid when you enter the US and not for the whole stay, I'm guessing that you probably want to extend your stay under VWP. If that's the case, then the answer is no you [cannot](https://www.uscis.gov/visit-united-states/extend-your-stay) extend your stay.

> You may not apply to extend your stay if you were admitted to the
> United States in the following categories:
> 
> Visa Waiver Program