Yes it can be possible, it all depends on the nature of the original recording, how it was mixed, what effects and post-production was done to the original, whether it is a Mono, Stereo or Multi-Track (i.e Quad or Surround type) source. If you are really lucky, some tracks are even available from gaming software sources that have the individual track separations! Another good source is to look at 'Alternate Takes' or mixes of a track that can be found on some 'Limited Edition' or 'Remastered' releases.
In the case of a commercial Vinyl, CD or MP3 source file, always try to go back to as close to the original release as possible, because any modifications to the track (format conversion, digital compression etc, can have negative impact on quality and how much signal is available to de-construct acceptable stems. Where possible, try to work with a clean DSD, WAV or, if you have to use a compressed format, FLAC rather than MP3 if possible, at the highest bit and sampling rate you can find. In the case of MP3 anything below 48/320 is going to give spurious results at best.
One Method would be to initially remove all the vocals from the recording. It is not necessary to always break each element of the original recording and mix the ones you want back again. Sometimes however this can also be necessary to remove the 'pumping' sound that sometimes happens to some tracks, or elements of a track in the same frequency range as the removed vocal stem(s), often due to the over-use of side chain compression in the original mixing or mastering process to raise the prominence of the vocals in the mix.
Use the same (or similar) process to separate the Lead vocal leaving the second and background vocals, and repeating the process until you achieve the desired result of having separate vocal stems for each part. This is not always easy, as even using AI software, the result is not always what you would desire (think of how long it took to get a sufficiently clean separation of just vocal and piano stems fot the Beatles 'Now and Then'!) . However, if you are able to separate all the elements, it is then just a case of discrete mixing of the relevant parts back into the instrumental stem.
Sometimes, you will find that after separation of the Vocals stem, the two separate vocals are actually panned left and right in the mix, often with vocal effects and/or 'soft' backing (think Oohs and Aahs) centered in the audio panorama. These may initially need additional effects, reverb or echo removal to take out any non-channel specific artefact before you selectively mix back the part(s) you require.
As to settings, there are no 'one-stop' basic options. You really do have to work with each track and apply whatever steps are required to achieve an acceptable end result.
Personally I use a mix of different stem separation packages, as so far I have not found one that does everything I need. UVR5, DeMix Pro, RX10 and Gaudio Studio are at present my go to applications. I also use Pro Tools, Logic or Audition to mix back the elements depending on what features I require for a specific track.