Using drip extraction, how much caffeine is extracted from coffee as a function of the amount of water used?
Caffeine has a solubility in water of 20% at 80 $^\circ$C, while the coffee has between 1 and 4% caffeine. 
That means that you have more than enough water to extract all the caffeine in the coffee. 
With the quantities you have given, I estimate that you are using from 12 to 24 mL of water per gram of coffee (bulk density 0.25 g/mL). 

So, it is not very likely that a change in volume will affect the total quantity of extracted caffeine much. Only the concentration per unit volume will be lower if more water is used. 
But then, solid-liquid extraction is not that perfect and possibly you will extract some more caffeine with more water. The main property that influences the extraction is the size of the milled coffee. The smaller the better is the extraction. 

Many other components of coffee are extracted fairly fast. 
Therefore, here we do a percolation (expresso) which extracts everything with very less water. The concentration of caffeine per unit volume seems to be higher, but the dose of coffee is much smaller.