Yes, it’s possible!
AM-1038 software recognizes the device connection port automatically. If you connect several devices to different USB-ports of one PC (activating PC-Link mode on each of them by keeping HOLD button pressed), run a respective number of the Software copies and press START button one by one in each Software you will see an independent data collection of the appropriate device.
The below screenshot demonstrates the example of simultaneous operation of 2 devices (one of them is in “µA” mode, the other one – in “mV” mode)