"If you or your colleague has" or "If you or your colleague have"?

Solution 1:

With a compound subject, the general rule is: If it uses "and", then clearly it's plural, so you should use a plural verb. If it uses "or", then the number of the verb should match the number of the LAST item in the list.

For example:

Either Bob or Fred has the answer.
Either Bob or the Thompson twins have the answer.
Either the Thompson twins or Bob has the answer.

(I haven't looked up a citation for this, but that's the rule I was taught in elementary school.)

Edit:

I see there is some disagreement, so I just did a quick search. Here's a link to a college grammar site: http://leo.stcloudstate.edu/grammar/subverag.html. They say:

If subjects are joined by or or nor, the verb should agree with the closer subject.

 

Either the actors or the director is at fault.

Subjects: actors, director; Verb: is

 

Either the director or the actors are at fault.

Subjects: director, actors; Verb: are

Solution 2:

‘The Cambridge Guide to English Usage’ says that in such cases notional agreement suggests the plural verb, but that it’s ‘less than an elegant solution’ and advises redesigning the sentence. Doing so here would require something like ‘Let me know if you have any questions, or if your colleague has any.’ In practice I think this particular sentence would pass unnoticed with the plural verb.

Solution 3:

For absolute grammatical pedantry, you could include both:

If you have, or your colleague has any questions ...

If you have any questions, or your colleague has, ...

However very few writers or speakers would go to those lengths.

If you or your colleague have any questions

... sounds most natural to me.