As many devices as you want can be controlled. If the devices are the exact same then it should be no problem to directly parallel the remote ON/OFF but if they have different types/standards then you may need to isolate each one with his own dedicated optoisolator and then the input of all those optoisolators can be controlled by one EXT IOx
The EXT IOx use the Toshiba TLP172 optoisolator so you can use the same one externally or something similar to control multiple devices and keep them isolated from each other.
If you do not have a soldering iron you can use the MRD-060D2 solid state relays for isolation so one of those for each device and then input of those controlled with EXT IOx.
EXT IOx can handle 50mA max so do not exceed that it is just an open or close circuit signal so you will need to have the battery in series with that to supply the input of an external optoisolator or the SSR like the MRD-060D2 mentioned before