The control amplifier on the cheapstat uses the TLC2264 op amp http://www.ti.com/product/TLC2264. According to the spec. sheet this has maximum output current of +/- 50mA.

You might be able to get output voltages as high as 3V if you only care about unipolar output. The cheapstat is a 3.3V device. The the potentiostat circuit uses the REF voltage as its effective "ground". The value of REF is set via DAC1 on the microcontroller. By default this is set to the mid-point voltage 3V/2 = 1.65V. This allows for symmetric positive and negative voltage output - e.g. -1.65V to 1.65V (at least from the hardware). You could modify the firmware and change the value of REF to be 0V. It which case you could output 0 to 3.3V. Also, you may need to make some other firmware changes - to the various test parameters - in order to get this to work.