A lot of people have the default view that developers are a congenitally greedy breed who can't be content with their base zoning entitlements. If you are one of these people, you should take a look at the chart below.
This is from a "zoning capacity" study prepared by the City's planning staff during the Imagine Austin process. The table shows how much land lies in each of Austin's residential zoning districts. It further classifies land as "developed" or "undeveloped" and "buildable" or "unbuildable." ("Unbuildable" here means roughly "unbuildable due to environmental features"; it has nothing to do with zoning-type setbacks. To calculate the "buildable" area, staff took the gross site area and subtracted the acreage burdened by steep slopes, flood planes, and creek buffer setbacks.) It provides a very precise total of the amount of land in the city available for development or redevelopment in each residential zoning district.
It's very weird that a majority-renter city like Austin reserves so little land for multi-family. Out of nearly 7,900 acres of buildable, undeveloped land in residential districts, less than 10% has been set aside for multi-family. Less than 1% of the undeveloped, buildable land has been reserved for the densest multi-famiy (MF-4, MF-5 and MF-6). Just 1.5 acres -- 0.0189% of the total -- has been reserved for the second-densest district (MF-5), and none at all for the densest (MF-6).
Things are just slightly better when we look at developed land. The city has just shy of 40,000 acres of buildable, developed land in residential districts. 11.8% of this land is zoned multi-family. But, again, just 1.5% of the total has been zoned for high-density multi-family , and just 87 acres (a little over 0.2%) for the highest density MF-5 and MF-6.
These totals do not include mixed-use. If you look at an Austin zoning map, you will see a lot of "MU" districts. But plain, vanilla mixed-use districts do not allow much density. The protypical mixed-use development is a "live-work" development with offices on the first floor and residences above. They are rarely multi-family projects. Dense multi-family projects are really possible only in vertical mixed-use districts, and then only if the developer provides the community benefits in order to obtain exemptions from the density restrictions.
Thus, if you want to build a dense, multi-family development by right in Austin, you've got slim pickings. Somewhere out there is an undeveloped 60,000 sf tract zoned MF-5. If you don't happen to own that tract, your options are to: (1) build something in a downtown CBD or DMU district; (2) build a VMU project (but only if you're willing to provide affordable housing); or (3) tear down apartments on some of the meager land already zoned for high density. Otherwise, you're filing for a zoning change or a PUD.