You're not supposed to be able to. You're only supposed to beable to switch region 5 (or 10?) time when you first use the DVD player, then you have to pick one and stcik with it. There are ways to change the region code afterwards, but they're not entirely on the level, so you'll have to look for them yourself.
You can't change regions directly. It is possible to buy a DVD player that is region free and allow you to play any DVD regardless of region. I am not sure how much they would cost since I don't have a need for playing anything other than region 1 DVDs but I would think that they are costed about the same as a regular DVD player.
you might be able to flash your dvd drive to a firmware with region-free ability, and perhaps some other perks such as if you have a Pioneer 117D in your powermac/emac you can flash it to a region-free, unlocked rip speed, 16x, etc etc. 108. i'm sure there are a lot of other drives you can do this with. does void your drive's warranty though, but not the rest of the computer afaik