@j.p.m. 

Hello.  I consulted our engineering team and they mentioned that with extra wires its most likely the outlet powers additional devices, like a switch or another plug.  You should be able to Wire the two black wires together and then the two white wires together, although as we have not encountered such a wiring before we would strongly recommend contacting an professional electrician to ensure no potential damage is done in the installation.  If you do contact an electrician for assistance we would greatly appreciate it if you could provide us the results of their findings.   

@j.p.m. Did you get this sorted out? I have the same situation and wired as described however I can not get the outlet to connect to my network. I've tried the ezsetup, the AP setup and neither work. I have other kasa devices that work fine.