The background to this discussion is that the Torah doesn't considers a person's body to be his to do what he wants with it. It is an instrument in the service of God.
Here is how the Nishmat Avraham reports on different poskim views on the topic (vol 2 pp. 60ff)
The Tzitz Eliezer forbids one to undergo plastic surgery in the
absence of disease or pain when the purpose is only to enhance a part
of the body. He writes that it was not for this purpose that the Torah
gave permission to heal and one may not allow a surgeon to injure him
for this purpose, nor is the surgeon permitted to do so. In addition
one may not put himself in danger, however slight, for such a
On the other hand the Chelkat Yaakov permitted a young girl to undergo
plastic surgery to straighten and reduce the size of her nose although she submits to bodily injury.
R Moshe Feinstein, in a similar case of a girl wanting to undergo
plastic surgery to make her look more beautiful so she could more
easily find a husband, answered positively quoting Rambam who only
forbids causing injury when the purpose is to harm, while here it is
to beautify her.
R Shlomo Zalman Auerbach writes that if plastic surgery is done to
prevent suffering and shame caused by a defect in his looks, it would
be permitted since the purpose is to remove a blemish. However if the
only reason is beauty it is not permitted.
In most cases therefore the discussion will be to what extent the surgery aims at addressing a blemish which creates mental pain and anguish and whether this is enough to overcome the obstacles above. To answer your question of "how far can we go and what can we change" one really needs to CYLOR.