ffmpeg : combine two or three audios into one by lowering the volume of the other
For the scenario mentioned in the question, use
ffmpeg -i audio1 -i audio2 -filter_complex \
"[0]atrim=0:10[s1];
[0]atrim=10:20,asetpts=N/SR/TB,volume=0.1[s2];
[0]atrim=20,asetpts=N/SR/TB[s3];
[1]atrim=duration=10,adelay=10000|10000[v2];
[s1][s2][s3]concat=n=3:v=0:a=1[b];
[b][v2]amix[a]"
-map [a] mixed.mp3
Usually, you'd want to use the sidechaincompress filter to adaptively reduce the volume of the music stream by analyzing the volume of the foreground audio.