Speaking about relevant aspects for the way sounds are being formed it comes down to the individual forms of the vocal cords, mouth, tongue, nose and lips as well as the way how they all play together when speaking.
The vocal cords thereby basically define the pitch in which a voice is perceived to be in whereas the timbre to refer to your wording is rather affected by the mouth and nose making a voice feel more or less nasal and probably defining also the loudness of the voice.
As I'm not really specialized regarding possibilities of manipulating this using only anatomical aspects I'll be focusing on digital manipulation of said characteristics. The pitch certainly can be manipulated by pitching a recorded part up or down - preferably using a tool like autotune which has proper algorithms running in the back to preserve the natural characteristic of a voice for as long as possible. The timbre might be changed using an equalizer to make certain frequencies more prominent or dim to adapt them to the voice that is being aimed for. As I can imagine each voice may lack certain individual freqeuencies that an other voice has (and vice versa) applying an filter algorithm that filters specific frequencies or shifts them might be also an option to achieve an approximation of different voices.
(Specifically in singing, not speaking.)
As in singing you often also come across the use of natural vibrato in a voice this might also be something notable. Manipulating this might be by far harder (if not even impossible) than previous mentioned manipulatable things - however someone with a more profound background regarding vibrato and its technical realization would be needed validating my point here. Logically for me it seems like applying a more or less realistic vibrato to a voice should be possible when the recording which you want to alter has literally no vibrato itself. Then you might be able to apply some sort of slight pitch automation (e.g. a LFO) to it. However you in this case you might want to make sure to apply the above mentioned methods (filtering frequencies, etc.) before applying any vibrato effects.
