The Great Highland Bagpipe has a range of only one octave + one note. Why is the range so limited, and would there be a way to increase it?
The number of notes depends on the number of fingers available to close holes with, remembering that you don't want to drop the pipe either. It also depends on the size of the hand.
In theory lengthening the chanter and adding holes would give a longer range. This might mean adding a key system so that more holes could be managed with a limited number of fingers. There is already a large difference in tone between the top and bottom of the range; this would be larger, but people could get used to that.
The piper obviously does not have the option of using lip pressure to change the note as an oboist does, and cannot change the air pressure too much either because of the effect on the drone pipes.
Why is the range so limited?
The part of the instrument responsible for generating the main notes is the chanter. That is the part the piper plays. The three drones, two tenor drones tuned an octave below the chanter keynote (low A) and a base drone two octaves below the keynote, do not change pitch.
The chanter produces notes according to the spacing of the holes and the volume of the pipe. These are low G, low A (usually in the range 470-480 Hz), B, C#, D, E, F#, high G, high A, so basically a D major instrument. The physical characteristics of the chanter (the volume of air inside it which can be set vibrating and the way that volume can change via the holes) determines the range and pitches available.
would there be a way to increase it?
Increase the length of the chanter and introduce more holes suitably spaced.