Trademark applicants in the US can file a petition to expedite their application under certain special circumstances. The petition filing costs $100.
As for the requirements for such a petition, TMEP Section 1710.01 provides the details:
Invoking supervisory authority under 37 C.F.R. §2.146 to make an application “special” is an extraordinary remedy that is granted only when very special circumstances exist, such as a demonstrable possibility of the loss of substantial rights. A petition to make “special” is denied when the circumstances would apply equally to a large number of other applicants.
The fact that the applicant is about to embark on an advertising campaign is not considered a circumstance that justifies advancement of an application out of the normal order of examination, because this situation applies to a substantial number of applicants.
The most common reasons for granting petitions to make “special” are the existence of actual or threatened infringement, pending litigation, or the need for a registration as a basis for securing a foreign registration.
Here are two recent examples, from the public records of the USPTO, of filings of petitions to make special:
The filing here includes a declaration from the general counsel for the applicant and attaches screenshots featuring the allegedly infringing product. [Interesting note: this matter concerns the configuration of hot air popcorn popper]