The answer if I understand the question is: it has been done a long, long time ago. Maybe not for metal detectors, but using one 'antenna' for multiple frequencies is old hat. One coil, no extra chips and a smart control head that tunes where you want it (within reason). Say you go with the harmonics with 3kHz as the fundamental:
>3kHz
>>6kHz
>>>12kHz
>>>>24kHz
>>>>>48kHz
Now that is quite a span on the spectrum, but the 'tuner' in the control head would center on the desired f, and tune the TX/RX circuits. Of course, as you know, the Eureka works at quite a span itself, and I think I have seen posts that talk of using a WOT on the machine. The hard part is making it equally effective at all desired frequencies. It might be a push to get one coil to work as good as a dedicated coil built around one or two frequencies. There are limits. The x series would be more popular if the chipped coils-thing was not in reality, a handicap (the real function of this 'chip' is disguised in technical nonsense that people parrot-all hogwash, and the rest is a big proprietary secret that the competition is too stupid to figure out). More stuff to go wrong and design around. A concept to improve upon. The Eureka is a much better machine to improve upon with a display, IMO. Darn good no display machine as is. If there were parallel resonant coils (Circuits), they would automatically select for the f in use. Would it harm consumers to know how something really works? Or is it better to treat them like mushrooms? If something is patented or Pat applied for, what purpose would the 'big' secret be? BS.
AND the coil is BLUE!
Cannonball