The best approach would be to use scan lists, with one scan list per switch device. This is when the switch device will set up a list of connections which are made upon an event occuring. For an example on how multiple scan lists could be configured, go to the NI-Switch Help in the section Multiple Module Scan Lists.
There are multiple approaches for this, either software triggered scanning, or hardware triggered scanning which can either be synchronous scanning, or handshaking. However, when using multiple switch devices, handshaking is not possible.
Software Trigger Scanning
Instead of having a trigger line connecting the DMM and the switch, the switch is programmed to switch prior to the DMM's measurement by utilizing the niSwitch Connect Channels VI. An example in LabVIEW demonstrating this, can be found in the Making Connections on a Switch (NI-SWITCH) vi. This approach can be employed for multiple switches, where each switch has its own scan list.
Synchronous Scanning
Each entry in the scan list is executed when the switch receives a digital pulse from the digital multimeter (DMM).
The DMM is programmed to take measurements at regular intervals and generates a digital pulse. The digital pulse is Measurement Complete (MC). This digital pulse is connected to the Trigger Input (TI) of the switch.
When the switch receives this digital pulse, it advances to the next entry in its scan list.
You must program the DMM interval time between measurements to, at least, the time needed for the switch to activate and settle.
An LabVIEW example for this is Switch - Scanning with a DMM - Synchronous (NI-SWITCH) vi.