My understanding is that you can, provided your I-140 was filed 365 days or more before the expiration of the 6th year.
Many lawyers sites say that you can extend your H1B if you have a
pending I-140 for more than a year, but I wasn't able to see this in the original Law text, and any USCIS memos. See below.
From the text of the
AMERICAN COMPETITIVENESS IN THE TWENTY-FIRST CENTURY act:
http://shusterman.com/s2045txt.html
SEC. 106. SPECIAL PROVISIONS IN CASES OF LENGTHY ADJUDICATIONS.
(a) EXEMPTION FROM LIMITATION-
The limitation contained in section 214(g)(4) of the Immigration and Nationality Act (8 U.S.C. 1184(g)(4)) with respect to the duration of authorized stay shall not apply to any nonimmigrant alien previously issued a visa or otherwise provided nonimmigrant status under section 101(a)(15)(H)(i)(b) of that Act on whose behalf a petition under section 204(b) of that Act to accord the alien immigrant status under section 203(b) of that Act, or an application for adjustment of status under section 245 of that Act to accord the alien status under such section 203(b), has been filed, if 365 days or more have elapsed since--
(1) the filing of a labor certification application on the alien's behalf (if such certification is required for the alien to obtain status under such section 203(b));
or
(2)
the filing of the petition under such section 204(b).
(b) EXTENSION OF H1-B WORKER STATUS- The Attorney General shall extend the stay of an alien who qualifies for an exemption under subsection (a) in one-year increments until such time as a final decision is made on the alien's lawful permanent residence.
Translated:
http://shusterman.com/pdf/h1b-pearson61901.pdf
E. AC21 106 -- Special Provisions in Cases of Lengthy Adjudication
AC21 106 permits H-lB nonimmigrants to obtain an extension of H-1B status beyond the 6-year maximum period, when:
(a)
the H-lB nonimmigrant is the beneficiary of an employment based (EB) immigrant petition or an application for adjustment of status; and
(b) 365 days or more have passed since the filing of a labor certification application, Form ETA 750, that is required for the alien to obtain status as an EB immigrant, or
365 days or more have passed since the filing of the EB immigrant petition.The Attorney General is required to grant the extension of stay of such H-lB nonimmigrants in 1-year increments, until a final decision is made on the H-1B nonimmigrant's lawful permanent residence.
The approval of I-140 doesn't affect your status, but filling I-485 + EAD will give you an AOS status with the permission to work (if you don't extend/use your H1B).
