The simple answer is yes, the  2 systems can work independently of each other without the belltpacks interfering with each other.
We recommend that you have both basestations set to ALL frequency mode and that the antennas of basestation #1 are at least 3-6ft apart from the antennas from basestation # 2
You can further improve system performance by setting one DX base to master mode and the other DX base to secondary base mode. This will allow both units to transmit in-sync and minimize RF clashesCheck DX basestation manual for full details

A beltpack can only transmit and receive when it isregistered to a base. During the registration process the base gives thebeltpack a unique algorithm key that allows it access to that exclusive wirelessnetwork and any wired intercom attached to the base. Bases with registeredbeltpacks cannot talk by way of RF to another base with registered beltpacksunless there is a physical connection made by either a 2 wire or 4 wireintercom port on both bases and those circuits have been turned on by way ofthe front panel switches.