An mp3 player is available (WolfjPlayer).
That mentioned, it is versatile but has its restrictions.
Although your question does trigger some ideas, i do think this would be a plugin to be developed by someone who has decent knowledge of the interior working of the system itself.
In regards to the multiple instances refered to, these things pop up in mind:
A) possible to attach a file or image: yes possible to hide from view> partial > would only be if ONLY members are allowed to see the post. (first would be all members> then could be divided in member access classes : eg all members can see all posts except the posts from another member class. There is (afaik) NO level to display all, but not seeing attachments >member classes)
B) the attachment is DATA so it will not trigger an audio player (or alike) (in regards to a) with extra step this could be achieved > attachment and audio player (direct play + download attach.)
(how i did it please by PM if needed; a user intructed how to do this can get this far; see the attachm. as a downloadable item if browser can not play the file ;-) )
C) the intended audio file should be a double piece eg. 1 for preview> limited time and 1 full file for dowload. Thus 2 attachments, a preview and than like b) a second one for full.. (can not be hidden). Link could be possible but only if url is known (at later stage, not by user;only admin > then download restrictions might be possible i guess).
D) An mp3 player that can see an attachment is an audio file posted in another part of the system..Hmm would need access to dbase and uploadfolder > multiple security issues will arise!!! open upload> file save? access granted to multiple sources etc..
I can comment further but it will be all related to give a user abilities, which envokes security measures, uploading, access to folders ( possible reworking) etc..
So being an admin on site i could get quite far with this, but that is not your question.
So my suggestion (as no such player or alike that is capable doing this in e107 presently) is looking at third party software (not always cheap);
that could do this leads me to Clone site products (think Pandora or Soundcloud). I must mention this is kind of standalone next to e107 (eg 2 sites). Those clones (not used, based on reading etc.) are already equipped with a lot you would like to do.
Than again as it will be 2 sites the need for login might arise for both in 1 go.. Possible? .
Conclusion: very good question !! helas i can not provide a solution (can play around with the Wolfjplayer, but do not believe it can, than again ideas triggered.. any way.. no answer from me in the near future to this.).
Advise: ask it here https://gitter.im/e107inc/e107 and maybe (will be a commercial item likely, iff someone would be willing to develop).