The range that is being measured is set by a monitor resistor that you can easily change from 1K to 100K giving you another 100:1 variation, although you need to switch the resistor in the process.
So, I've ordered INA169 from Adafruit. What were you thinking with the "monitor resistor"? There are two resistors on the board, the shunt, which is 0.1ohm and the load resistor, which is 10kohm.
Keep the shunt resistor but set it up so that you can change the load resistor. Adafruit's breakout has a 10K surface mount resistor in this position but also has pads for a standard 1/8 axial lead resistor. If you want to swap values to extend the range, then you can use an 'n' way rotary switch with the common to the active side of the circuit and your various load resistors wired between the respective switch selector pins and ground.
3 resistors will do it: 1K, 10K, 100K. Alternative approach is to have 100K permanently wired and then simply switch in a parallel resistor that will yield 10K & 1K with simple on/off switches but these will be harder to find. 1K in parallel with 100K is probably close enough for the accuracy you'll get with this setup. 11K (10K+1K) might be close enough as well... This second approach has the advantage of always having at least 100K in the load resistor position as you switch.
Tom