There's no need to do this, nobody does this since AES is safe.
If you do not want to use AES-128 use AES-256 or AES-192. If you do not trust AES, especially if you do not have a processor with support for AES-NI, use another cipher, such as Serpent-256, Salsa20, or ChaCha20.
The only security gain would be if the algorithm alone is vulnerable to exhaustive searches, such as DES. In this case there is 3DES that does exactly 2 encryptions and 1 decryption, but there is still the problem of meet-in-the-middle .
3DES was created because DES is vulnerable to exhaustive searching. Using the same process for AES is useless, AES does not have the same problem. In addition, the AES is safe even against quantum computers, if you prefer flow figures Salsa20 is also second to PQCrypto .
I believe there are other issues you might be concerned about, such as information integrity or key storage, for example.