What happens if you plug more than one charger in the new MacBook Pro (2016)?

The system will choose the power source that provides the most power, and it will not draw power from the others.

Apple has released a support article (and another one) describing this:

• Your MacBook Pro draws power from only one power supply, even if more than one is attached—so using multiple power supplies will not speed up charging.

• If you connect multiple power supplies to your MacBook Pro, the one that provides the most power will be used, regardless of the order in which you connected them.

• You should not connect any power supply that exceeds 100W, as it might damage your Mac.

They don't push power (watts) but they do push VOLTAGE. And if a charger pushes the wrong voltage, bad things can happen to your device.

The voltage is negotiated between devices (e.g. charger/mac), but if the charger is non-compliant, bad things can happen.