change job at the end of 6th yr H1B?

This is my 6th year of H1B and my current employer has filed LC for me in Nov 2004,and I already filed the 7th year extension since my Labor has filed for more than one year. Now there is a better job oppotunity and the new employer is willing to sponser to keep my status, but is it possible to work out? Thanks for your kind suggestions!