If the sound of the currently running show is interrupted by a further show starting in addition to it (Add Mode), both shows presumably use the same stereo output. The following rule applies: The show to be started last takes over the stereo output from the currently running show.
Solutions:
Always use separate outputs for simultaneously running shows. Using an SC Master 4, both signals can be applied to one stereo output via the internal mixer and a routing of Multi-channel 4 2.
With an SC Master 6/16 you also use separate outputs, joining them again via an external mixer.
For any other cases it may be useful to think of an elegant way to cover up the abort of the music by turning down the volume slowly via a Special Functions marker and turning the volume up again after the new music has started. See Remote-controlling volume and sound.