Depends on the box. I have the new Virgin Tivo box and I think you can record 3 channels at the same time as watching another one. Google it sweetcheeks.
I have the latest Sky+ box and you have two cables coming from the aerial into your box. This allows you to watch one program and record another, as it has done for years. You can record 2 programs at the same time but not if you are watching a third. With muti-room you can have several tvs showing different programs but it doesn't increase the recording capability. As far as I know.
You can record 2 at the same time, as long as you are watching one of them. Or you can record 2, and watch a 3rd which has already been recorded (on your planner), as long as you leave it on the same channel as one of the programs to be recorded whilst you watch the recorded one Clear as mud