Is it safe or even possible to hook up 2 different types of inverters in a series to power more appliences?

Here is what I would like to accomplish. I have a gas powered champion 2000 watt portable inverter generator that I want to connect to the 12 volt (deep cycle) battery while the battery would power additional 12 volt power inverter (pure wave) 4000 watts. I’m trying to power over 5000 watts total household... show more Here is what I would like to accomplish.
I have a gas powered champion 2000 watt portable inverter generator that I want to connect to the 12 volt (deep cycle) battery while the battery would power additional 12 volt power inverter (pure wave) 4000 watts.
I’m trying to power over 5000 watts total household items.
Simply said AC to DC to AC = more power? Yes or NO?
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