If you use Spleeter you can isolate vocals and BGM. Maybe you are at that stage already. The problems you still need to solve, assuming you want them to blend aesthetically, is key and tempo. For this you will need to detect the key and tempo each part is in. Then you'll need to adjust the tempo and key from one or both parts to match. Even then you will still likely have a clash of structure where the verse and choruses don't match up or even worse structure dissimilarities. For this you need another neural net like Spleeter but trained to combine various structures of music, or of course you could do this part by hand.
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If you use Spleeter you can isolate vocals and BGM. Maybe you are at that stage already. The problems you still need to solve, assuming you want them to blend aesthetically, is key and tempo. For this you will need to detect the key and tempo each part is in. Then you'll need to adjust the tempo and key from one or both parts to match. Even then you will still likely have a clash of structure where the verse and choruses don't match up or even worse structure dissimilarities. For this you need another neural net like Spleeter but trained to combine various structures of music, or of course you could do this part by hand.