Look at it as a physiology problem. The ear can identify the notes that make up the chord because critical parts of the brain have been taught that the combination of notes that make up the chord; the fundamentals present in the chord, and their several harmonics (overtones or partials), as well as the 'beating' interactions will give you the sound of the chord. Also there are 'amplitude' issues. That means that the higher pitched notes that make up the overtones are generally much lower in amplitude that the fundamental that generated them. The key point,- the brain, in its own wonderful way, was taught to recognize that chord. BTW - how the brain does that is a whole other discussion, very interesting, but very complicated. So that is what a piece of 'machinery' would have to imitate.

However when you try to imitate that with 'hardware' you are stuck with the problem that you will have three or possibly more fundamental notes and then all of there harmonics all interacting.

Possibly you could create the spectrum of the chord which, theoretically, will show you all the notes, - the fundamentals and the several (or many) harmonics including 'aplitude' interaction. Then possibly you could pump that data into a good, high performance processor and use some very elegant AI type software. The software would analyze the list of individual notes, put each fundamental together with its harmonics, isolate the beat generated notes, account for amplitude differences and them present to you the result. The most interesting result would be the list of the original three or four notes that went into the original chord. The program you'd need is really the 'alter-ego' as it were, of what the brain was taught to recognize the chord.

Hope this helps.