In the Mp3tag Tools section, there you can utilize any command-line utility, which can move a file from here to there, for example the DOS command MOVE, this works for single file selection.
As an alternative method you may let create a batch command file via the Mp3tag Export section, which can support multi files selection too.
For now I use the simplest and most obvious way: I have chosen to move one file to my "FOLDER B" which is located in "FOLDER A". Mp3tag do remembers this location, even if I close it and run it again,;so every next time I have only to choose either to stay in that folder or move up one level [or down]. And it also remembers a separate location for coping
This of course works best with a "single line" of sub-folders", but for my moving purposes is absolutely enough