"Can the UNO receive multiple power inputs"
No. The auto-power switcher will select the voltage at the Vin pin as the current source if Vin/2 >=3.3V.
"thinking dc 5.7V via usb"
This 5.7V would not be regulated down to 5V, and you will stand a good chance of damaging the ATmega chips which are not recommended to be powered from more than 5.5V (5V +/-10%)
Aren't the shields designed to either from the 3.3V pin, or take in 5V or Vin and make their own 3.3V or 5V as needed?