When I enabled iCloud Music Library on my iPhone, I had the option of merging it with my existing music. I did that, and my phone has both music from my iTunes library and music from Apple Music on it.
Now, I want to add some more music from my iTunes library to the phone.
Before I enabled iCloud Music Library, there was a setting in iTunes that let me pick a playlist to use to sync (Settings -> Music). Now, with iCloud Music Library enabled, that option is gone and there's just a toggle to sync voice memos. And I can see a way to edit my phone's music library (On My Device -> Music -> Edit Playlist), but when I drag an album into it, nothing happens.
I was able to work around this by doing the following:
Disable iCloud Music Library on my iPhone
Plug the phone into my computer
Sync with iTunes
Disconnect phone from my computer
Re-enable iCloud Music Library on my iPhone, and pick Merge again.
So obviously this is possible, but there has to be a better way than this. The last step, especially, takes a while. And, it looks like I need to tell it t ore-download all of the Apple Music songs if I want to listen to them offline.
I found this on Apple's website, but it involves turning on iCloud Music Library in iTunes, and I don't think I want that.
I also found this question but it seems the advice there is to repeat the steps I outlined above.