One apple, one orange, or two bananas are then added to the blender. Two bananas, one apple, or one orange is then added to the blender.
Check out this embarrassment:
[W]henever the president or the governor issue [issues] an executive order . . . . Bob Dunn, Contemplating Our Future, Tex. B.J., May 1992, p. 448 (quoted in Garner Legal, p. 841).
As you'll see in chapter 6 of the eBook Understanding the Parts of Speech, this rule also applies to the either . . . or and neither . . . nor correlative conjunctions. Thus, number is governed by the number of the noun closer to the verb. Look at these examples:
Neither the coach nor the players want to lose. Neither the players nor the coach wants to lose.