Loop and mix audio on video
It works if you mix audio separately.

ffmpeg -y -i test.mp4 \
-f lavfi -i amovie=bg_sound.mp3:loop=55555 \
-filter_complex "[0:a][1:a]amerge, \
                 pan=stereo|c0=0.5*c0+0.5*c2|c1=0.5*c1+0.5*c3" \
output.flac