A registered mark or a mark for which an application to register has been filed shall be assignable with the good will of the business in which the mark is used, or with that part of the good will of the business connected with the use of and symbolized by the mark. Notwithstanding the preceding sentence, no application to register a mark under section 1051(b) of this title shall be assignable prior to the filing of an amendment under section 1051(c) of this title to bring the application into conformity with section 1051(a) of this title or the filing of the verified statement of use under section 1051(d) of this title, except for an assignment to a successor to the business of the applicant, or portion thereof, to which the mark pertains, if that business is ongoing and existing.