You can convert almost any current output to a voltage output by adding a resistor across the output terminals. Calculate the resistor such that the voltage across the resistor at max current does not exceed max input voltage of the acquisition system. Also, check the specs for max output voltage of the signal source. Don't expect the circuitry to supply more than the circuit supply voltage minus, say, 20 p.c.
Of course you will have to compensate the offset - at 4mA 'live zero' output you will of course get a reading different from zero. This should be possible by software.
However, if you need an excitation voltage higher than supplied by the board you can use an external power supply. Maybe you will have to use a grounding scheme different from what be used with an 'internal excitation' source (from the board).