There can be confusion as to the capabilities of a 2 pole matrix. Although there are 2 signals paths for each row and column point these points will be switched as pairs.
Each crosspoint is implemented by a relay(s) that have 2 independent contacts controlled by one control line - both contacts will either be open or closed at the same time and a circumstance where one is closed and the other is open once settled is a fault condition. If you selected a crosspoint connection between X1 – Y1, X1.1 would be connected to Y1.1 and X1.2 would be connected to Y1.2. You cannot split the connections.
There are some occasions when 2 pole switching is implemented by relays which are not in the same package - usually because that type of relay is not available as a 2 pole relay. In these cases the design maybe arranged so both coils are driven by the same control line or that the software aggregates the coil drives so they behave as one control.
So why would you want to use a 2 pole matrix configuration? This configuration makes sense in a number of situations.
The first is when you want 2 pairs of lines, for example when using a matrix for 4 terminal DMM measurement. In a 4 terminal measurement you may connect Y1.1 to V+ and Y1.2 to I+ with Y2.1 to V- and Y2.2 to I- for a 4 terminal DMM resistance measurement.
A second example is when you are switching a voltage source and are using remote sense to ensure regulation at the UUT is being sensed - the two pole arrangement ensures that the sense connection follows the power connection.
Two pole operation of power supplies also makes sense when controlling earth currents, the flow and return of power supply currents is better controlled if the power supply uses 2 pole (or 4 pole with sense) switching. The switch topology also tends to reduce the radiation of signals since the effective area of radiation antenna is better managed.
There are also cases where a source is required to be connected as differential system - in this case the switching system may also have a controlled differential line impedance. However, be wary to not assume that a two pole switch makes a good differential switch since the transmission line impedance is not controlled unless the design is specifically created for switching differential signals. A switch system designed for differential operation is also likely create lower emissions and have better crosstalk than a switch simply designed for 2 pole operation since in systems designed for differential operations tracks are routed in close proximity and have a greater distance to other signal lines. That means that crosstalk injected on to one signal line is likely to be similar in magnitude to that injected in the other signal line, thereby introducing a common mode signal rather than a differential signal, and on emissions if a victim path is well enough separated from the differential signal then the emission signals approximately cancel. An examples of true differential switching is the Pickering Interfaces 40-736.