Getting into the same mind as your fellow improvisers is tricky, but pretty awesome. That's one of the reasons when I'm looking for new members for our team I often look for people with good social skills instead of good "accomplished" actors.
There's this social psychology term called the "Chameleon Effect," which refers to people's natural ability to mimic each other. Maybe you've seen this with people you've got good rapport with--you naturally mimic each others' speech inflection, body language, etc. Interestingly, the most likable people tend to mimic the most. And, that's why likable people are often really good at improv--because they get in sync with the rest of the team.
Anyway, that was a little digression. There's a funny game where people respond to a question at the same time, saying the exact same thing. It might sound impossible, but with a little practice, and if you're on your teammate's wavelength, it gets easier.
Here's a funny example. There's 2 rotund improvisers who are answering at the same time, and they're even wearing a single shirt, which makes it even better.
2 Headed FAT Man Improv Comedy - Click here for funny video clips