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We don't actually know.

If it could change his looks, it's a bit puzzling that he didn't do so, because the whole point was to hide out from aliens who could follow the TARDIS, and knew what he looked like. (Obviously there are good behind-the-scenes reasons to have David Tennant play John Smith, but those don't explain why he looked like David Tennant in-universe.) But it's always possible that he was comfortable in that body, and didn't want to be hampered trying to adjust to a new body when he had so much else to deal with. Or that he's just a little vain, and liked looking like David Tennant.

Similarly, the Master seemed happy to get out of his Derek Jacobi body and into his John Simm one after regenerating, which makes you wonder why he wouldn't have chosen a different body when he first used the chameleon arch. But then again, he might have wanted to look distinguished and harmless when he was hiding, and just didn't want to look like that anymore now that there was no more war to run away from. Or maybe he just associated that body with his Yana disguise, which he considered weak and un-Master-ly.

So, we don't really know. We've only seen the arch used in two episodes. He also used it in the comic The Forgotten to recover his stolen memories, and he briefly considered that Jackson Lake in "The Next Doctor" had used it to hide some but not all of his memories. Other than that, we know nothing about its capabilities.