Sync Apple Music but keep my own collection!

Hi all!

so here’s what I’d like to do with Apple Music: I have my music collection on my phone, built up over many years, including many obscure things not available on streaming services.

i want to be able to play this whenever I want- it’s all on my phone.

But also add things to my library from Apple Music that I like? And create playlists that I can share across my devices? But “syncing “ my library means Apple finds all my music collection online, so I can only play it online! I don’t want this! I want my own offline collection available PLUS ability to add things from Apple Music to my collections…can I do this?

hope you understand what I mean!