Can I write my PhD thesis based on another student's paper if I'm a co-author? My supervisor asked me to write my thesis based upon one paper which I'm co-author on. I was told to take results which were not published and extend the figures. I was also told to include some figures from the paper after I ask the journal for copyright permission, extend the discussion in the paper and insert all of this into my thesis. After all of this, I need to do one more experiment. 

Is this usual in science and for a Ph.D.? What precautions should I take in this case?
"Can I write my PhD thesis based on another student's paper if I'm a co-author?"

I feel a difference between the question title and the question content. It boils down, to me, to "were you a notably active contributor to this paper"?

If the answer is yes, and you take care about rephrasing published text, re-drawing figures, you can reuse the results. A thesis should be personal, and show your personal contributions. A PhD thesis based on only one paper is not uncommon in mathematics, yielding short theses. In other domains, you can expect to write one or two chapters for a published paper, by extending results, adding experiments. Not a whole thesis.

If the other student's contribution is significant enough, he should be acknowledged in the chapter introduction for instance: "this chapter is based on a joint work..."

If the answer is no, I am afraid it could be a case of plagiarism, and loose ethical behavior.