In general, moving companies that do the following are required to have interstate operating authority (MC number) in addition to a DOT number:

• Operating as for-hire carriers (for a fee or other compensation)
• Transporting passengers, or arranging for their transport, in interstate commerce
• Transporting federally regulated commodities or arranging for their transport, in interstate commerce

FMCSA operating authority is also referred to as an “MC,” “FF,” or “MX” number, depending on the type of authority that is granted. Unlike the USDOT Number application process, a company may need to obtain multiple operating authorities to support its planned business operations. Operating Authority dictates the type of operation a company may run and the cargo it may carry.

You can register online via the FMCSA Online Registration System.

Source: http://www.fmcsa.dot.gov/faq/what-operating-authority-mc-number-and-who-needs-it