Beef up inverter by adding more mosfets?
Not as simple as that. Adding more MOSFETs would reduce conductive losses but the increase in switching losses could kill MOSFETs. But gate drive capability is limited and adding more MOSFETs would slow down the rise/fall time of all transistors thereby increasing switching losses and MOSFETs could starting dying because of this.
There are also ringing and oscillation issues since the additional MOSFETs will probably not have optimal PCB placement nor will the additional MOSFETs have their own dedicated gate components (which should not be shared amongst MOSFETs since MOSFETs can ring amongst themselves).
The wiring, traces, bulk capacitances, snubbers, and current sensing circuits (if there are any) will also not be designed for the higher currents.
Another major problem is that the transformer probably will not be able to handle the extra power required.