Yes, but only the rental half qualifies for 1031.

Would you have to allocate any of the down payment (all from the proceeds of the sale of the rental property) to the personal residence half of the duplex?  If so, could this create boot?

Are there 2 purchase contracts or one? Does each half of the duplex have the same FMV?

There would be one purchase contract.  I would assume that each half of the duplex would have the same FMV.

Then I think everything would have to be half rental, half personal residence.

They have not yet sold or purchased the properties.  Is there a way to structure these transactions to defer the entire gain?

Not if one of the acquired properties is a personal residence.

"to defer the entire gain?"

You told us this: "The value of the rental property is close to the value of half of the duplex"

As you know, the entire purchase cannot be in the 1031. The like kind part of the exchange will be able to be computed, but we don't know what "close" means. Higher? Lower? Because it seems "close" to half the new property, which makes it "nearly" the entire rental half is either more or less. Depending.

The sale of the rental might be $225,000 and the duplex might cost $500,000.  The part of the duplex being rented out might be valued at $250,000, so the new investment property is valued higher than the sale price of the rental.  So if all of the proceeds are used to purchase the duplex would there be any boot?  Would some of that down payment need to be allocated to the personal half of the duplex, and create boot?  Am I thinking about this the right way?

Which of these did you decide was the solution?