Can I selectively breed my sourdough starter?

Yes, but it might have other effects that make it less effective as a leaven.

When I was experimenting with sourdough in the past year or so after a long hiatus, I had a pretty good batch going and parked half in the fridge, then had some life events that caused the part that was out to be left 24 or more, not 12 hours between feedings, and it turned very, very sour - but it also didn't do much for raising the bread.

Unless you are fixated on getting there via sourdough, I'd suggest picking up some citric acid if you like your bread "as sour as possible" - though even that might do in your yeast if you use too much - of course, there's always really sour flatbread, I suppose, by either method.

Given that you are working with a combination of bacteria and yeasts in a "wild yeast" culture, it's going to be very difficult to specifically engineer that. Indeed, the tendency is that, eventually, whatever wild yeast combination is native to your area eventually infiltrates or even takes over most cultures.

If your just looking for a little bit more "sour" you could try "sour salt," which is pure citric acid. Some view that as cheating, but as an enhancement to a natural sourdough culture, as opposed to trying to fabricate it, entirely, it comes out not tasting forced.

From what I read in Flour Water Salt Yeast, if you let your starter ferment at lower temperatures it should encourage the production of acetic acid, which is more "sour" than lactic acid normally produced by your lactobacilli.