H-1B is initially valid for three years, and previous to the expiration of that three-year period, you may extend your stay further by applying for an additional three years. Generally, after you have extended your stay for the entire six-year period, you cannot extend your stay in the United States beyond that point. Even if you are petitioned by different employers, the six-year limit remains.
There are exceptions to the six-year period limitation in cases where the person has experienced some kind of delay in the adjudication process. Individuals who have delayed applications for labor certification or employment-based visa petitions, and those who haven’t been able to adjust their status due to the backlog of their preference category can be eligible to extend their stay in the United States beyond the usual six-year period.
If you wish to obtain legal permanent residence in the United States it is important that you begin the process to obtain your green card as soon as you have secured appropriate employment.