Secure multiparty computation... where one entity owns all parties Here's a corner case for you. 

A user produces a small amount of confidential data and would like to delegate a third-party to perform some computation on it and return the results. Data and results are to be kept secret from the third-party, you can assume a "curious but honest" threat model.

My first naive intuition was that this would be an obvious application of FHE, but now I wonder... is there any way to tackle this use case using sMPC instead? 

In other words: split the input data into a number of "workers" which are all controlled by the same third-party. Is there any sMPC scheme that is robust to such a scenario?

Thanks.
No.

If you split the data between the parties, say using additive secret sharing, anyone controlling all parties can recover the full data. That is part of the very definition of secret sharing. If you want to ensure that the data will remain hidden even when the adversary controls all parties, then you cannot simply run a secure MPC protocol on shares of the input, you need something that will hide your input even when the state of all parties is known. Homomorphic encryption is indeed the most natural solution that comes to mind.