This is what some of us do with our inverters but only plugs into one of the Inverter 120VAC receptacles.
My floorplan layout

I have two Inverters in my trailer one is 1500Watts and the other is 600Watts both are PSW... The 600W just has two multiport receptacles places in the trailer to plug into when I need "emergency" power. I dont have enough enough batteriey power to run my second 1500WATT invert to full power so I only really use it as a backup for the 600WATT one. I do however sometime plug the shore power cable into it to just gain access power to my trailer recepacles. I have to flip some breakers in the panel to keep from overloading the inverter when I do this however...
I want to add a flip lid connector near my shore power cable on the outside of the trailer which is wired to the 1500WATT Inverter. This way I could just use a short 15A to 30A adapter to power up the trailer when I do this...
would look something like this.... This is my poor man transfer switch
the center flip lid connector is my shore power connection - the flip lid ocnnector on the right goes straigth to the 1500WATT PSW Inverter.

If you could answer 2OLDMANs question he might have some more info for you. I'm thinking you will NOT be able to parallel those two sides of the 120VAC receptacles.. The manual should tell you... Maybe we can look that up on this side if we had the model number of the Inverter.
Roy ken