You can easily achieve population densities of 10k/km^2^ (25k/mi^2^) with townhouses up to 4 floors, each with a backyard, and a couple parks and plenty of public spaces and ample public transit as well. This density will fit 1 million people in a radius of 6 km. Add in some apartments and you'll boost it even more. For this, in most cases you don't need an elevator, and you don't even need reinforced concrete. In fact the goal is to be less dependent on fosail fuels or the grid, not just for getting around town, but for entering and leaving your residence, and maybe even in the construction of it.

In terms of shapes I'm mostly talking about the footprint not being just a simple rectangle with each floor congruent to the ones above and below it. Much of it would still be close to rectilinear, but there's a lot you can do with that. Smaller floors toward the top open up the possibility for green roof balconies. Overhangs are broadly used in German timber-based vernacular architecture. Archways and courtyards are everywhere in planned units.