I moved multiple times in 2023. SC, DC, SC and then finally IL. Turbotax won't recognize that I was in 4 total places. How do I get it to understand?

You don't...details are critical though.

Most likely, you'd have to indicate you moved once to IL on the date you moved there...from SC.

You'd file part-year SC for all income before the move to IL, and Part-Yr IL for all the income after the move.

Then you'd treat the time in DC as-if you were working there as a Non-resident  (i.e you didn't really "move" there permanently.....since you didn't.)

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SC does part-year folks differently than most states....SC allows you to file as:

1)  either a full-yr resident...calculating a tax on ALL your income for the year, then allowing a credit for taxes you paid to DC and IL

or

2)  As a full-yr non-resident, where you define exactly what income you received during the time you lived in SC.

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Either way could get messy, and take a couple weeks to get right.

...or, maybe past time to get a local PRO to file for 2023 taxes?   (not a seasonal storefront. A real full-time pro)??  Maybe.