Can I power 1 leg of a 240v single phase panel?

My inside panel has 240v single phase coming in (L-L-N). My stove and electric car plug use 240 volts, so they draw power from both 120 volt legs. I would like to install an inverter for automatic battery backup on the 120 volt leg that powers "essential" circuits. Is this possible to do without having to relocate the 240v circuits?
Thanks.
Thanks.
Comments
Another possible issue, is overloading the neutral wire since there is no other phase to equalize the power. Maybe someone else can explain it better than I.
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I think the easiest way around would be to run a 120v sub panel right next to your main, with all the loads you believe to be essential. Connect it to the main panel through a transfer switch, You may even be able to use an inverter pass through as your transfer switch, that would automatically charge your batteries and transfer the loads when there was a failure.
- Assorted other systems, pieces and to many panels in the closet to not do more projects.
https://www.homedepot.com/p/Reliance-Controls-30-Amp-10-Circuit-Manual-Transfer-Switch-310A/206499407?MERCH=REC-_-searchViewed-_-NA-_-206499407-_-N&
You basically connect to your main panel. Disconnect a branch circuit and wire "to" the transfer switch. Then wire the same circuit from the transfer switch to your disconnected branch circuit with a wire nut.
I did this with my home... But I got a 6 circuit version--And I really needed more circuits for backup connections.
You can use the "single" generator connections to connect to an AC inverter+Automatic transfer switch pretty easily... And just leave the above transfer switch in "Genset" position--And let the Inverter/AC transfer switch combo power the above transfer switch as needed. And you can always bypass the inverter to utility power by switching back to normal.
There are quite a few different version of this boxes.
-Bill