In some circumstances, this is possible. In "The Stolen Earth"/"Journey's End", the Tenth Doctor regenerated without changing his appearance or personality (in effect, he regenerated back into his existing form). He did this by ending the regeneration early, after it had mended his body but before it could transform him. The presence of his spare hand was essential to this and, without it, the regeneration would have changed him. As he explained, "Used the regeneration energy to heal myself, but soon as I was done, I didn't need to change. I didn't want to. Why would I? Look at me. So, to stop the energy going all the way, I siphoned off the rest into a handy bio-matching receptacle, namely my hand. My hand there. My handy spare hand."
Additionally, the conversation between the Eleventh Doctor and the Curator near the end of "The Day of the Doctor" suggested that it is also possible — or will at some time become possible — to regenerate into a past incarnation; the Curator appeared identical to the Fourth Doctor, only aged. He hinted at this to the Eleventh Doctor but did not confirm it explicitly, let alone give any details of how or when.
"The Then and the Now" (comic story), published by Titan Comics, showed different incarnations of the Doctor, including the Curator, attacked by an enemy down his timeline. This more or less confirms the Curator's identity.