Can I start an application as another user without actually switching users?

Question

Is there a way to start an application as another user so that the started application would use the other user's preferences/history/resources et al?

For example: I've logged in as Alice and I'd like to start Firefox as Bob, so therefore Firefox would show Bob's browsing history instead of Alice's.

I tried

$ su Bob
$ open -a Firefox

But with no apparent effect; as a matter of a fact Activity monitor shows the Firefox process is being run by Alice—not Bob.

I understand I will need Bob's login credentials, but that's not a problem.