I am not familiar with that "all in one" unit, but like most others, the inverter part gets power from the batteries and then the panels either recharge the batteries, and/or supplements the batteries. So in full sun your 4 panels will barely be able to provide the power for the cooler. But that is what the batteries are for. The more batteries, the more load they can take up. Maybe someone else can run the exact numbers to be a bit more accurate. Adding a fifth panel in parallel won't hurt the combo unit. The unit will only draw as much power as it is able to. But as someone else noted, the cabling will need to be beefy.
12AWG 1 Pair Solar MC4 Y Parallel Branch Connectors MFF&FMM Pair
12AWG 16.4FT Solar Extension Cables Wires with Female and Male MC4 Connectors
6AWG 13 Inch Battery Interconnect Cable-two wires of 6 awg on each cable.
If these all have to be replaced and I have barely enough power to run just the cooler, then perhaps the cheaper route is to replace the inverter/controller but need help to know specs. Would want to set them up to get as much watts as I can.