Direct Music Player audio to Caller Assume you have a call. I would like to play a piece of one song to the caller at one point of discussion, while keeping your voice too in the discussion. 
I am using Android 6.0 CyanogenMod with Samsung Galaxy S4. 

Edited: According to Media Playback's docs, the standard Android system does not allow the feature. 
However, I am interested in how this restriction works. 
If the feature works in non-rooted CyanogenMod, then it is not a restriction. 
Also, I am not sure if Media Playback's manual applies to the whole system. 

How can you direct Music Player's output into the ongoing discussion?
You cannot

Media Playback developer documentation says (emphasis added)


  You can play back the audio data only to the standard output device. Currently, that is the mobile device speaker or a Bluetooth headset. You cannot play sound files in the conversation audio during a call


Edit

In response to your edited question:


I am not aware of Cyanogenmod permitting this- searching in their source code may give a clue
To enable this, I presumed would require programming, so searched Stack Overflow and found this Why it is not possible to play an audio file on a voice call in android. This gives a couple of reasons, in answers as to why it is not possible - security and prioritization of audio
It also suggests ways of  achieving which are in programmers domain