If the aircraft is airworthy and you feel comfortable in that make and model then by all means go for it. We're pilots, not english majors
That said however, whenever you decide to fly a privately owned aircraft, as a couple other guys have pointed out, make damn sure you personally review all logs, mx records, and the aircraft to ensure airworthiness. I've caught a number of paperwork issues on planes that are owned outside of my employer. Usually it's a quick fix, missing signature, etc, but make sure everything is good to go before you fly.
Secondly, just because you've got the CFI and are legal to teach in the airplane, doesn't mean you're safe to teach in the airplane. Find your personal limits and stick to them. It's not worth losing your certificates if something goes south just to get a few extra hours of dual given.