First of all you won’t get very far using filletedge command. It’s capabilities are very limited.
Filletsrf on the other hand is very robust command but since McNeel has refused to add any automation to this process you will have to do each and every step manually. But it is still much faster and more reliable then making fillets with blends and/or sweeps.
The easiest way to deal with those corners is to make the one fillet
crossover the other. See enclosed file.
Fillet_crossover.3dm (307.5 KB)
All four corners can be done as crossover fillets (shown in red). Two of the corners you can crossover the natural extension of the fillets and the other 2 corners you need to steer the fillet extension inward so that the other fillet can crossover it. There is another recent thread that has an explanation of how that is done.: