Here's how I would think about it; Each LED is a 20mA device @ 2V. So, the effective resistance is 2V/.02 = 100Ohms. That figure can be highly variable. What you want is a device that limits the current and decreases the circuit sensitivity to variables. For a first-order approximation, the origial circuit had a 5:1 ratio between the "fixed" resistance and the "variable" one. That's pretty good, IMO. So, I wouldn't cascade more than about two LED's with the given voltage. And more then two, and I think you'd need a higher supply. Alternatively, you can run the LED's at a lower current, and still get pretty good illumination from them. Good to experiment a little to get the best results.
For a better result, there are sensitivity equations that involve taking derivitives and forming ratios. Even then it's a judgement as to how much "sensitivity" you can tolerate.