So long as the look is only one look, it is a look, not a looks. So long as the person is a single person, they have a look; they do not have looks unless their appearance changes. This does not include a change in clothes, in that case, you would say that there are multiple looks which a person wears, not that they themselves have multiple looks.
The person is their body and their body has one look at any given time so they have one look until their body changes at which point they will have had multiple looks, but they can never have multiple looks at the same time; therefore, “She looks good” does not mean “she has good looks” but rather “The look that she is presently presenting is good.”
If you mean to say something referencing all of the looks which she has ever had and has the possibility of presenting, you should say, “At any given time, she possesses multiple outfits capable of creating a plethora of appealing looks.”