Editing PDFs attached to notes

I have saved several PDFs to Notes on my Mac. When I open them in Preview I can highlight passages. But Preview insists it can't save these changes to the original document, so I have to save a new version elsewhere. This is very inconvenient. I guess I'll have to keep all the PDFs in the cloud somewhere with links in Notes. Can this really be the way Notes is supposed to handle PDFs? Am I missing some functionality here? Thanks for any help!