Can a petitioner amend a new claim into a pending federal habeas petition after the expiration of the limitations period?

A habeas petitioner may amend a new claim into a pending federal habeas petition after the expiration of the limitations period only if the new claim shares a "common core of operative facts" with the claims in the pending petition. Mayle v. Felix, 545 U.S. 644, 646 (2005). "[A] new claim," however "does not 'relate back' to the filing of an exhausted petition simply because it arises from 'the same trial, conviction, or sentence.'" King, 564 F.3d at 114. Stated differently, a claim does not relate back "when it asserts a new ground for relief supported by facts that differ in both time and type from those the original pleading set forth." Hebner v. McGrath, 543 F.3d 1133, 1138 (9th Cir. 2008).