DDC112 Analog to Digital converter
With this AD converter you don't change the gain, instead you change the speed of the integrator by changing the capacity of the integrator. With a greater capacity you must provide a higher input current to get the same reading.

Some capacitors are provided on chip and you can select them with the range pins. When necessary you can provide an external capacitor for each integrator.

Given these informations one can conclude that the lowest range with the highest sensitivity is given by the chip and it's design. If that is not enough for your application you must either provide an input amplifier or use another, better suited, chip.

Please read again pages 9 and 10.