Yes, you can report a 1031 Exchange with multiple relinquished properties in TurboTax Premium. I recommend you use TurboTax Desktop software if you are going to report a 1031 Exchange so that you can access and use the Forms mode, which is only available in the Desktop Software. For more information, see TurboTax Desktop Software
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Note, TurboTax Community posts do not like the format of IRS website links; it thinks they include phone numbers and removes it before posting 😐 Hence, I cannot link directly to the instructions for reporting Multi-Asset Exchanges.
You can manually search the 8824 instructions for Multi-Asset Exchanges.