If you’re willing to incur some tax, you may purchase less than your net sale under IRS Section 1031.
And, you may take cash out without jeopardizing the entirety of your 1031 exchange.
However, if you want to purchase less than what you sold or take some cash out, then the IRS will call that “booty” and tax it as profit. The IRS is willing to leave its tax in the game, but they are expecting you to leave your profit in the game as well. So, there’s no taking your “booty” and buying an island without paying at least some tax.
The IRS considers this taxable because their interpretation is that the first dollar you take out is going to be a dollar of profit.