For those who don't recognize the part number, the MM-PM15-403 is a PanelMate 1500 HMI brand labeled as Modicon.
I'll need more information about what its connected to in order to give you a more definitive answer. The answer to your question is "maybe". Generally, HMI units, particularly those of that vintage, are communications "masters" and the PLCs they communicate with are "slaves". That means the HMI is the entity that initiates all data exchanges between the themselves and the PLC. The PLC only "speaks when spoken to". It's a lot easier to have one HMI communicate with two or more PLCs than to have two or more HMIs talking to one PLC.
If your PLC has a second serial port, you may be able to use that to communicate with an additional HMI.
The "it depends" part is because that particular model had a Modbus Plus daughter board as an option. If the existing unit is using Modbus Plus, then it is possible to add another HMI to the same network. I don't know the distance limitations off the top of my head.
The PanelMate 1500 could also have an Allen Bradley Data Highway daughter board which would also permit additional HMI units on the same network.
Regardless, that HMI is an old unit, no longer in production.