Simplifying Meet-In-The-Middle Attacks
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!.