The idea would be:

    key = get_key()
    classic_key = derive_key(key, "domain-classic")
    qc_key = derive_key(key, "domain-qc")
    ciphertext_a = classic_encrypt(plaintext, classic_key)
    ciphertext_b = qc_encrypt(ciphertext_a, qc_key)

I think this is different from what you wrote but I can't really tell.

FWIW I am not advocating for "encrypt twice" at all, I'm just trying to understand.