Not sure if I'm trans but I have a full on intersex condition called PAIS, or approximately the completely ambiguous genitalia with non-virilizing puberty.

In the end there are two developmental pathways. Male and female. There is no conceptually valid description of a third pathway, because human sex is a reproductive concept described by exactly two gametes.

There are a few processes within each pathway, for example the male pathway is driven by primarily by Testosterone, Dihydrotestosterone, Androstenedione, Anti-Mullerian Hormone. The female pathway by Estradiol, Estrone, Progesterone. These hormones are produced by the gonads, which are differentiated as ovaries or testes by SOX9, the production of which is promulgated by SRY. All of these things can get jumbled in any number of ways.

The thing is though: a human does not actually have a sex except in an abstract sense. We are just lumps of meat and bone. We merely express a collection of developmental outcomes from the male and/or female pathways. All of these outcomes are necessarily contained within this bimodality.

To give a simple example of this; XX isn't your sex, nor is XY, so XXY and X0 and XXX and so on, are also not your sex. We could say that having a penis is your sex but maybe you also have a uterus, so why isn't that your sex? I have tested but I couldn't develop as a male, so tested and ovaries are also not really your sex. And I couldn't produce gametes of either variety. We could potentially argue for three sexes, those who make sperm, those who make ova, and those who make neither. But that's not really a useful definition either. And so on.

The point being that there is no such thing as being a third, fourth, or fortieth, unique new sex.