fully homomorphic encryption with information-theoretic security?
You said you don't need to conceal the set of transformations that have been applied.  In that case a simple scheme is

$$T(\text{Enc}(x)) = \langle T, \text{Enc}(x)\rangle,$$

where $\text{Enc}$ is information-theoretically secure encryption (e.g., the one-time pad).  In other words, you simply list in the cipher text which transformations should be applied to $x$ after it is decrypted.