Do you think it might be possible to add 2 (or more) bits of precision to the DAC?

Code:
Interval  #1  #2  #3  #4
     DAC  00  00  00  00  -> 0.00v
     DAC  00  00  00  01  -> 0.04v
     DAC  00  00  01  01  -> 0.08v
     DAC  00  01  01  01  -> 0.12v

     DAC  01  01  01  01  -> 0.16v
     DAC  01  01  01  02  -> 0.20v
     DAC  01  01  02  02  -> 0.24v
     DAC  01  02  02  02  -> 0.28v

     DAC  02  02  02  02  -> 0.32v
     ........