But TPS introduces genetic variability. And a quirk of most potatoes is their polyploidy. Most normal plants have pairs of chromosomes. But most 'modern' potatoes are tetraploid, they have double the number of chromosomes, which gives rise to all sorts of genetic mixing if they reproduce sexually through the flowering-cross polllination-setting seed route. This genetic mixing has the possibility of developing all sorts of interesting characteristics in the offspring.
It is possible to cross potatoes, using a similar method to tomatoes - emasculate the female parent by removing the anthers pefore they shed pollen, collect pollen from the male parent, then apply it to female parent stigma. Rather than go through all the mechanics of this, check out the information at Tom Wagner's tater-mater blog, or Rebsie Fairholm's excellent daughterofthesoil blog.
Alternatively, if you have a variety that flowers readily (not all do) and that has no self-compatibility problems (many do), and that retains its fruits to maturity, you can just see what turns up. That's what I've done.
My TPS, in this generation at least, is from self pollinated Pinkeye potatoes, derived from some certified seed tubers I purchased at my local nursery (sourced from Goodmans Seeds, if I remember correctly). There is a slight chance they have crossed with another self-propagated potato that just came up in my garden nearby, which also set a fruit, but it wasn't flowering at the same time as the Pinkeyes, so the chances of an intervariety cross is slim.
Sow it like tomato seed, and prick out. That's where I am now - a bit risky at the start of autumn, since these little plants really need to set a tuber between now and winter, so I have something to plant out next spring.
I'm also intending on growing out some plants to do a bit of crossing next season. A greengrocer in Melbourne stocks a good range of vegetables, so I bought a couple of tubers of all their interesting non-standard lines - Pink Fir Apple, Virginia Rose, Blue Zarr, Royal Blue (which look the same), and Gold Finger.
Hopefully they will flower, and I'll get some more interesting colours to throw into the mix.
I've already got Purple Congo and another couple growing in the greenhouse, so I'll see what happens with their flowering phenology over autumn/winter.