XLR is two cores and a shield.
The two cores carry a positive and negative of the same signal. Any noise picked up shows as a + or minus on both cores, so when one is inverted (to make the signals the same) the noise cancels out.
You can't send a signal down the shield cable; That's no good.
It's common to all inputs and connected to the chassis of the interface. That's connected to ground so your signal would go straight to ground.
If there was going to be a conceivable way of doing it it would be to use the + for one signal and the - for another, but even then the preamps circuitry is gonna be balanced and it would involve a shitload of DIY, and your inputs would now be unbalanced.
I don't even know if that's possible, but if it is you'd be so balls deep that you may as well just built an interface with more channels.