Security issues of a MAC-then-Encrypt-then-MAC approach?
Using a MAC on the plaintext may potentially leak information about the plaintext (MAC algorithms do not necessarily ensure confidentiality of the data they are applied to, although some MAC algorithms like HMAC seem pretty safe). If you want to avoid this (theoretical) problem, then you should encrypt the MAC on the plaintext (i.e. MAC-then-encrypt, not MAC-and-encrypt).

As long as you encrypt the inner MAC along with the plaintext, and the key for the inner MAC is unrelated to the key for encryption, then it is "obvious" that this inner MAC does not induce extra trouble; that inner MAC can be viewed as some plaintext redundancy. (In fact, you could replace the inner MAC with a simple hash function.)

Having two MAC algorithms still seems wasteful, in CPU and data size. If the problem you are trying to fix is a wrong decryption key in an encrypt-then-MAC setup, then a more efficient solution is to derive the encryption key and the MAC key from a single master key, using a KDF. If you do that, then, when the MAC matches, you know that you used the right MAC key, and, by property of the KDF, you also know that the encryption key is the right one. It so happens that deriving encryption and MAC key from a single source with a KDF is a very common situation; so the problem of "lack of plaintext integrity" does not happen in practice. This is why the construction with two MAC you are alluding to does not appear to be much studied.