Can I repeatedly Awaken something in order to give it a variety of languages?

So, the Awaken spell must be cast on a beast or plant with int of 3 or less. For beasts, it has the following permanent effect: "The target gains an Intelligence of 10. The target also gains the ability to speak one language you know." It has a casting time of 8 hours.

The Feeblemind spell will, among other things, reduce the target’s int to 1 for a duration measured in months. The 4d6 psychic damage is nontrivial, but still manageable. Feeblemind does not appear to do anything to known languages, and can be cured with Greater Restoration, Heal, or Wish.

Would it be possible, then, to repeatedly Feeblemind and Awaken something so as to give it an arbitrary number of spoken languages? (Assuming you could get the assistance of reasonably high-level druids who knew the various languages in question.)