You don't state how your sources were mixed. If we are talking about multitrack session with sources panned in place (the kind of studio mix popular in the seventies), separation works very well.
If we are talking about a single multitrack session with master tape available where we want to deal with bleedover into the "wrong" microphones, stuff is still doable.
If you just have some "acoustic" recording of the whole band where the "mix" happens by being in the same room, stuff is pretty hopeless for enjoyable results: you can still achieve improvements if the aim is preprocessing for the sake of recognition tasks.
"Song with acoustic guitar and string synth" tells very little: does "song" imply "singing" as well? How many microphones were used? Is the synth mixed in as a digital track, as an analog input track, or was it also present in the acoustic signal? How much digital and redigitized and analog post-processing was done?
At any rate: in our current time copyright law is so abysmally stupid that you need to negotiate for every trivial sampling of everything, so if you are thinking about commercial remixing, you can try just to negotiate for access to the original master tapes as well if that would help.
So it might make more sense to restate your question in reference to a much more specific scenario: in "I have a song with acoustic guitar and string synth" is too unspecific with regard to "song" and too unspecific with regard to "I have": what kind of material/media do you actually have, and what kind of legal situation do you actually have?