The same way we all do--sign up with a whole lot of companies and see who has shops in your area. Look beyond your area on their job boards when possible and see if they are shopping the client in other areas--a good indicator they are likely to shop the client in your area but the jobs already taken in your area. Build yourself a list of who shops whom both in your area and in other areas.
Sometimes you can get an inadvertent hint by reading through forums. Somebody may be talking about doing a shop at ABC client (without mentioning the MSP doing the shops) that you know who shops ABC client. Somebody else may chime in and say that when they were doing XYZ client for the same company they found that . . . You now will know that the MSP shops both ABC and XYZ.