How would I implement randomly selected, additive music?

Question

I've been trying to think through this myself, but I think it's time to ask for help. In the game I'm working on, there are 3 worlds with 15 rooms in each. I would like each room to introduce a different layer of music from 3 random choices. Those choices would then be "remembered" and played in the rest of the rooms in the world. For example, the first room would choose one stem from 3 options and play only that. The next room would play that stem and another one randomly chosen from 3 options. So on and so forth.

I've tried watching multiple tutorials and reading documentation, and I start to have a better idea of what I'm doing, but ultimately I just end up a little more confused. Thanks for the help!