Yes, you can do that. Just make sure the cables between the batteries are sized for the full inverter load and connect the Positive to one bank and the negative to the other. You will also want to consider how you parallel each bank.
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2003 Winnebago Adventurer 38G F53/ V10 605 watts of Solar
1999 Winnebago Brave 35C F53V10 Handicap Equipped
1999 Jeep Cherokee, 1991 Jeep Wrangler Renegade and 2018 Chevrolet Equinox Diesel
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