If you're reading this, you should've already read the article on how to move folders. If you haven't read that article, please click here before continuing with this one.
As a Business user, you also have the ability to move folders between team catalogs. This works the same way as moving a folder into My Songs, but instead of selecting My Songs, you select a different team catalog. You can navigate through the folder structure of any team catalog that you have access to by clicking on the arrow next to the team catalog in the modal.
Important things to remember
Folders are only allowed 6 levels, so you won't be able to move a folder that would break this rule.
Folders cannot be moved into folders that you have View Only access to.
Moving shared folders will have an affect on members. Before a move is final, you will be alerted if people will be affected.
Members of a shared folder will gain access to any folders that are added to it. Before the move is final, you will be alerted about the change in sharing.
If you have a lot of folders, you can use the search feature on the Move modal to find exactly what you're looking for.