These are not additional sexes.
For example, a male with Klinefelter syndrome (XXY) is still male.
> Let's say we had the ability to genetically re-engineer people into whichever sex they wanted
We do not, nor anything even remotely close to that.
Only by arbitrary definition of the abstraction we use. If we instead defined maleness as the ability to inseminate women and produce viable offspring they wouldn't count. If we defined it by having male genitalia then people with androgen insensitivity syndrome wouldn't count.
Male and Female are human terms we've chosen to categorize animals, but nature doesn't give a flying fuck about our definitions.
> We do not, nor anything even remotely close to that.
Obviously. This is called a 'hypothetical' or a 'thought experiment'. We use these to test the suitability of our mental frameworks of understanding. In this specific instance, I'm asking you to pretend this is true to see if your reasoning holds up, of if there is cognitive dissonance suggestive of a flawed model.