The comment by Rory that the proxy would have to use a self-signed cert if not stricltly true.
The proxy could be implemented to generate a new cert for each new SSL host it is asked to deal with and sign it with a common root cert. In the OP’s scenario of a corportate environment the common signing cert can rather easily be installed as a trusted CA on the client machines and they will gladly accept these “faked” SSL certs for the traffic being proxied as there will be no hostname mismatch.
In fact this is exactly how software such as the Charles Web Debugging Proxy allow for inspection of SSL traffic without causing security errors in the browser, etc.