Short answer is no - sorry. Since you have mentioned the client, ICA contracts and the forum guidelines prohibit the linking of the client with the MSC.
My advice would be to keep signing up with companies, and then making a list of what shops you have found with those companies. As you have already found, clients change MSCs all of the time so if you are signed up with a bunch of companies, chances are that you will find these shops again. And by signing up with different companies, you may find a shop you like better for someplace else. I've had that happen.
I know it's a tedious process, but in the long run it will pay off. In the meantime, you could check job boards that post jobs for multiple companies. Presto has Sassie companies, and there is also MS Job Board, Job Slinger, and iSS. Kern also does scheduling for multiple companies also. Hope you find what you are looking for and more!
Kim
Post removed as it breached the Forum guideline which states, "Do not reveal the clients of mystery shopping companies". Additionally, it is an ICA violation to name both the MSC and client. Feel free to repost.