"Can I have a word?"

Although, strictly speaking, they CAN have a word...

If they asked whether they 'may' have a word, then you could say "No".

They are actually actors, reading words that someone else has written. They do not have to be polite all the time.

They can, Aka... but only the one!

People ( like my DD) who confuse may and can, and shall and will, drive me potty!

Well, yes...not disputing that.
(Although I am not Aka)

Oh! And should, shall, also!

That was to Grannyknot.

Oh, Galen, stop interrupting!

Oops, sorry, Ana. My point is that it is never just one word, so, being pedantic, it should be "Can I have lots of words!"

I love all this pedantic ness , just love it !!

[

Would n't sound quite the same if she said, "can I have a long drawn out discussion with you" though would it.

Add yer own "please"

It was a boring Silent Wtness this time. I thought.

Actually, having thought further, you're right Grannyknot. If someone asked you if they could have a word, and you replied 'No', that would complete the transaction!

Perhaps the appropriate reply would be "Of course you can. How about – pandiculate?"

Show off.

Alright for you. You're fresh out of bed.

Ana posts crossed. I was NOT interrupting

We are all interrupting.

Pain in the bum Innit.

I hope you're not addressing me jingle. It's nearly midday; I've been up since six.

Oh. Yes, well. It's bedtime here. Night night/have a nice rest-of-the-day

/

Pish!

Can I have a word? is an idiomatic expression. It doesn't need to be perfectly corect grammatically.

That said, my parents always replied to Can requests that should have been May with: You can but you may not.

Answering a straight no to the request in the OP would be out and out bloody rude.