MPC is $f(E_1(a), E_2(b)) = c$, where $E$ is encryption by different keys $k_1$ and $k_2$.
Homomorphic encryption is $f(E_1(a)) = E_1(c)$, where the input and output are encrypted.
I want $f(E_1(a)) = c$, because I'm going to use $c$ but can't see $a$.
One user will give me private inputs, I'll run a computation and get the results in plaintext. It seems to fall between MPC and FHE. Is there a technique that can do this?