Yes you can have a ladder like this for any resolution you want (4, 5, 8 ,10, 16 and so on).
The problem with going to higher bit counts is the resistor matching. The more resistors you use the tighter they have to be matched to each other. With normal 1% resistors you will not get more than about 6 bits and maintain monoticity.
That's interesting Mike. I suppose that error from resistor matching will just adds up error more and more to the ladder as whole until you stop adding resolution bits?
I guess that if you really need to rely on math to expect accurate results a DAC chip is the way to go and not R/2R ladders.
By the other hand ladders can be useful (even for more than 6 bits or wathever), if you can accept constructing a calibration table from empirical measures, I mean when you don't need direct math processing out from ladder outputs but just input/output know values.
I had a interesting experiment on this some months ago assembling a simple synth. I wanted the synth to be able to play exact notes in a 5 octaves range and I got it playing exact notes after scanning (or finding), exact notes (voltages), on output by trying input values. It was a R/2R ladder tied to 2x VCO's and was able to tune perfect notes this way. To be able to find exact note frequencies (exact as 0.5Hz of tolerance), in a 5 octaves range I needed a 14bit ladder. This is some result about this experiment: https://soundcloud.com/rodrigonh/vc