The EB-3 case involves three steps: the Labor Certification (LC), the I-140, and green card application.

First, the LC is filed with the Department of Labor. Generally, the LC process is not eligible for expedite. You can check LC processing times here.

Once the LC is approved, the next step is the I-140 immigrant petition with USCIS. The I-140 is eligible for premium processing. Under premium processing, you can receive the I-140 approval within 15 days of filing unless a Request For Evidence is issued.

The final step, the actual green card application (either adjustment of status if you are inside the U.S. or Consular processing if you are about the U.S.) is generally not eligible for expedite.

If you are an adjustment of status applicant, your Employment Authorization Document (EAD) and Advance Parole (AP) requests will also be submitted with the I-485 application. USCIS will accept expedite requests of the EAD and/or AP in certain, very limited situations. Please reach out to your attorney if you would like to discuss expediting your EAD or AP. Please note that the expedite request would be an additional service fee that you will need to pay directly to the law firm. There is also no guarantee that the expedite request will be successful. For general information on emergency travel and expedite requests, check out this resource from USCIS.