The partnership could do a 1031 exchange for a different property, the individual partners cannot do a 1031 exchange with their individual ownership.
Partnership Interests Excluded From 1031 Exchange Treatment
Unfortunately, as we have learned over the last few decades, partnerships cause significant planning problems for partners and their tax advisors. Partners are not permitted to sell or dispose of their partnership interest and subsequently defer the payment of their capital gain taxes by acquiring like kind replacement property through a 1031 Tax Deferred Exchange transaction.
Partnership interests are specifically excluded from 1031 Exchange treatment under Section 1031 of the Internal Revenue Code. Partnership interests are personal property, and are not considered to be like kind to the acquisition of real estate, even though the underlying assets held within the partnership are in fact real property.
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