I don't think housing is one of the few (if any) goods where increased supply drives up cost, nor do I think there is any evidence this is the case.

You are eliding two different kinds of goods here: units of housing, and land. The average price of the former would presumably decrease. The average price of the latter would presumably increase, since loosened restrictions on development would make it possible to build more units of housing on a given lot. For current owners of single family houses, it's likely that the land price effect would outweigh the unit effect, although there will be exceptions (the dynamics of exurbs will be different from those of central areas, for example).

Out of curiosity, what would be a good where increased supply drives up cost? I can't reason any off the top of my head.

Induced demand is a thing. Not sure to what extent it applies to housing in any particular market, but any destabilizing effects of rapidly adding more housing should be seen as artifacts of the fact that we've let this problem go unaddressed for decades. People need places to live, and if we don't serve that need then the problems are only going to get worse and the solutions more disruptive.

There are also less visible efficiencies in having people living close to their work, like roads that aren't crammed with cars because people don't have to spend three hours behind the wheel every day getting to and from work, and the additional productivity that comes with all that extra time.

Induced demand is where more of some good is supplied, which drives down its price, which increases the amount consumed, which means the price isn't driven down as much as it would have been if there had been no change in amount consumed. (A common example is widening a congested highway: more capacity reduces congestion somewhat, which means that the inconvenience of driving on that highway goes down, so more people drive, so the congestion doesn't go down as much as you'd naively predict.)

What I'm not seeing here is a way for increased housing supply to make the prices go up, as opposed to down, but not as much. Network effects, maybe: increased density of a city could make being in that city more valuable, thus making more people want to live there at any given price, which means that prices would rise.

Yes, that's what induced demand is.

In a vacuum, no, I don't think simply adding housing can meaningfully drive up prices. But (as you say) obviously it feeds into organic urban growth, which does increase demand, so you have to keep building housing. It seems that the problem we have in our big tech hub cities is that we let that growth happen for a while and then decided that there would be no more housing.

I can imagine an induced demand effect as whole new classes of people realize that they can actually now live close to where they work, and come flooding back into the city. But like I said, that's an artifact of artificially constrained supply.

"Induced" demand is a misnomer for latent demand becoming measurable. It's a signal that a change was good but not enough; backpressure is reduced but not yet zero.

That would be Giffen good, which may not exist at all.

https://en.m.wikipedia.org/wiki/Giffen_good

Not really. Probably closer to a Veblen good (which does exist) but, in any case, those are about increased price driving up demand, not increased supply driving up price.

(I suppose increased supply could drive up price if providing that additional supply increased the overall costs but you'd presumably still be constrained by the overall supply/demand curves of the market.)

Simple economics tells me it does. Care to explain?

Best you are going to get on here is something like "increased supply doesn't lower prices in the housing market duhhh" without any actual reasons.

The demand in city is probably inexhaustible practically speaking

The burbs however....