Is it possible to swap out the OEM inverter for something larger? Can the stock wiring handle more amps with a larger fuse?

 

It's always bad practice to increase the capacity of an automotive circuit by only increasing the rating of the fuse.

According to the 2012 JK service manual, the feed wire for the OEM inverter is 14 AWG. That's not very large. I would not feed a larger inverter with the OEM circuit.

 

What ronjenx said. You're better off installing your own inverter with proper gauge wiring and fusing.

 

I agree. I remember when I was a young kid using light gage speaker wire for something in a car. Once I turned the key, the entire length of the cable instantly smoldered with the insulation melting off. Use the proper gage wire for the number of amps you plan to carry, and use a fuse that will blow before your wires melt.