As I recently reported, iTunes 12.5, currently in beta and due for release in the fall with macOS Sierra, will improve the way you can tag and organize classical music in the app. You will be able to tag classical music with work names and movement names.
The way iTunes displays the names of classical works will change. While the “song name” will still be part of a track’s tag, iTunes will display an “aggregate” name if you have entered information in the Work and Movement Name tags.
If you wish to use this system for organizing your classical music, it will take a bit of work to apply your existing tags to these new fields. Fortunately, Doug Adams has created a couple of AppleScripts to simplify this.
One of these scripts copies the text of the Name Tag And Places It in the Movement Name tag. Another script performs a similar operation with the Work Name tag.
Remember that iTunes 12.5 is still in beta, and this tagging may change. So even if you do have access to the beta version of iTunes 12.5, I wouldn’t recommend rushing to change tags on all of your classical tracks.