I'm sorry for double-posting, but I got it working
What I did was making 7 multi_manager, each would turn on one of the songs and turn off the other and trigger the trigger_changetarget (also 7 of them). I've named the trigger_changetargets tgt and the multi_manager mm.
When the button is pressed, it triggers mm1 (triggers song1 and tgt1 (changes button's target to mm2)). When its pressed again, it triggers mm2 (triggers song1 to stop it and plays song2, and triggers tgt2 (changes button's target to mm3)). It does this for all 6 songs, then a 7th mm and tgt are added.
When the button is pressed at last, it triggers mm7 (stops song6 and triggers tgt7 (changes button's target back to mm1, repeating the loop))
I figured it out after looking a bit about multi_manager and trigger_changetargets on teleport destinations, it made me think about the situation on a song spectrum. Thanks for the help!