They likely won't allow the double booking. I've also received emails about overlapping flights - even when those were not exactly the same flight numbers. So having two flights ATH-AMS a day apart is still enough to trigger the mechanism and be flagged. Surely you can then explain to them that you are doing back-to-back flights, however in your case - it being exactly the same flight - is not possible.

If you really cannot cancel or transfer one of the two I would suggest calling them and asking if there is an option to convert one of them into an "extra seat" for comfort or transport of an musical instrument. Then at least you'd have an empty middle seat. If that would work...I'm not sure. Pretty sure that there is a procedure and that 2nd ticket should be booked in a different way/name - but you may be able to get that changed.