When we refer to "remote I/O", we are generally meaning a remote I/O master talking to a base with an EBC100 or a drive with an EDRV100. When used with an EBC100/EDRV100, I/O can only be controlled by one I/O master. I/O masters are either ERM100 or Do-more's built-in remote master.
If you are not using an ERM or Do-more's built-in master, either EBC100 or EDRV100 can be accessed by Modbus/TCP, and yes, more than one device can access it.
I would *not* have more than one device attempting to write the remote I/O. My preferred implementation would be to use Do-more's I/O master, and then have other devices get information from the Do-more controller itself via Modbus/TCP, rather than trying to talk to the I/O.