Simplifying Meet-In-The-Middle Attacks Considering the fact that a block cipher is a bijective function on the set of possible plaintexts, if one views the encryption of a  datum with a key $K_2$, which has been already encrypted with the same n-bit block cipher, using key $K_1$ as a single n-bit mapping $\text{F(plaintext}, K)$, is not bruteforcing through $2^n$ keys not more efficient than performing a Meet-In-The-Middle Attack (or MD-MITM, as the case may be)?
This question asked for the DES years ago. To achieve this kind of attack you need to first show that the target encryption algorithm is closed under functional composition i.e. forming a group.

The easiest might be is showing that it is not forming a group as in DES.

Although you may get one $K$ for only one block with the negiligible probability it will work for the other blocks. 

Actually, we don't expect such property exists for good block ciphers. The keys, as you remember, select one permutation from all possible permutation randomly. What you are asking is a very specific cipher which is not random.

In short, It is not expected!.