newbie Q: "Stacked" public key algorithm

sorry for the stupid question. Up to now I was just a cryptography user
without really understanding the technique behind, but now I've a question
regarding a solution I'm looking for, a kind of "stacked public key

Image, a company has a public and a secrect key. Employes also have their
own key pair. The planned scenario is like that:

the employee (Alice) send her public key to the company.

the company "mixes" their own private key with the public key of Alice and
send it back to Alice. Let us call this the "mixed key"

Alice can use this "mixed" key together with her own private key to read
messages with where encrypt with the company public key, means messages
which were "sent do the company".

But Alice should not be able to seperate the company private key again out
of her mixed key, so that she can't give the company private key alone to
somebody else without telling that she was the one who forwarded the
company secret key.

Do you understand, what I mean? Has anybody ever heard about such a

Good question, isn't it?

Any hints are appreciated & many thanks in advance

best regards