I assume your goal is for each E-Stop switch to kill power to all motors and signal the Mach 3 controller.
Each box would need to be modified to accept an external E-Stop signal, output an E-Stop signal to the other box and to signal Mach 3. This is not a trivial task. Details of each box will have to be known to plan the modification. It would be difficult, if not impossible, to obtain enough extra contacts to add to the existing E-Stop switches. Adding a small relay to each box can provide extra contacts.
Power for the relays would need to be available when the boxes are off. This means a supply not switched off in E-Stop mode.
Contacts from the relays would be substituted for the E-Stop switch contacts in each box.
The E-Stop switches contacts could then be used control the relays.
Contacts from each relay would be wired in series to signal the Mach 3 controller.
A simpler way to protect your machine would be to add an additional E-Stop circuit that kills power to the two boxes and signals Mach 3. More than one switch could used. The new E-Stop switches would need two contacts, one for power, one for Mach 3. The switches on the boxes would not be used in an emergency.