Please forgive me if this is a basic question, I'm in high school so I still don't understand very much.
Let's say there are two servers, each with a set of public and private keys. These denote server one: $PK^1, SK^1$ and server two: $PK^2, SK^2$. Each of the private keys stored on the servers are encrypted with the opposite public key. The private key on server one is encrypted with the public key of server two. The private key on server two is encrypted with the public key of server one.
Data $(D)$ is sent to server one encrypted with $PK^2$. Server one encrypts $D$ with $PK^1$ $D = Enc(PK^1, D)$
$D$ is sent to server two, where $D$ is decrypted so that $D = Dec(SK^2, D)$. This should mean that the data is still encrypted with $PK^1$. Server two sends the data back to server one, where server one gets the plain text by doing $D = Dec(SK^1, D)$.
The benefit of this should be clear, the hosting provider is unable to see either of the private keys, which is a massive benefit to software such as Tor. If a private key of a hidden service is stolen, it is disastrous. This way there is no chance of that happening, unless both of the servers are compromised.
Is encrypting a secret key and being able to decrypt plain text with it possible?