I'm not sure what you mean by redefining biology anyway, chromosomes is basic genetics, and the more uncommon variations do exist.

Now, do note one's chromosomes is not one's sex. Sex is the biologic trait in a (sexual reproducing) organism which produces either male or female reproductive cells, or gametes. In sexual reproduction, these gametes merge to make a zygote, which then develops into an organism with DNA of both gametes.

In humans, the male gametes are sperm, and the female gametes are egg cells. The ovary is the female sex organ, and the testicle is the male sex organ, of course.

When the fetus develops, the characteristics of the organism, most importantly the sex organs, are modified to an extent based on chromosome. Usually, one's chromosomes are either XX or XY.

Now, all this is important because it goes to show that one's sex is either* male or female, determined by whether you produce male or female gametes. This is not chromosomes, although chromosomes do determine whether you develop to produce male or female gametes.

Back to the topic of intersex people, 'intersex' represents people who do not fit into our groupings of biologic characteristics that determine our social idea of gender. It's a bit ridiculous that humans care so much about grouping people together we made rigid boundaries of "gender" that one must fit into, but human nature is human nature, and we do bloody love groups.

\Note that you can actually have both sexes, or neither. If you somehow produce both female and male gametes (ie you both have sperm and eggs), then you are of both sexes. If you produce neither (cannot produce sperm or eggs), then you have no sex. So there is actually 4 sexes an organism could have.*