Mixing mp3s?

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Lacking the satisfying information about mp3 encoding techniques I would like to know whether there is a definitive yes or no answer for the following question:

Is it phisically (or logically) possible/impossible to mix .mp3 files without decoding them first?

Example: I have a piece of music in multitrack format, each track in mp3. I would like to get the whole music mix as quick as possible, avoiding dealing with big size files.

Thanks for any answers.

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Forgot to mention, that the reason why I need this answer is that I am trying to set up a web project, where multiclient mixing of different versions would be possible. (So at the end of the day I will need a linux-command-line program to mix these mp3 parts)