When I was growing up I would ask my mother, "Can I have some juice?" She would correct me and say:
" No, Greg. It should be 'MAY I have some juice'. 'Can' is about ability, and of course you have the ability to have juice. The question is ... are you allowed to have juice? So you should ask: "MAY I have some juice?" "
So I grew asking 'may I' and not 'can I'.
And when I learned to speak German, I automatically applied this convention there too. I recall a specific occasion when visiting Zurich, and I went drinking with some German-speaking colleagues. The waiter arrived at the table and I asked "Darf ich ein Bier haben?" (May I have a beer?) Everyone looked at me, and laughed.
In German, the convention is actually "Kann ich ein Bier haben?" (Can I have a beer?). And unlike in English where "may" is good manners, in German it's like asking permission from the waiter - to see if he thinks it's OK for me to have a beer! And apparently it sounded really funny to German native-speakers.
Of course, since you're learning Mandarin, you're probably aware how difficult (and wrong!) it is to translate directly from English. This applies in terms of vocab, grammer, and of course culture.
And in this case, if you're ordering a beer in Chinese, you don't ask "May I ..." (ke yi), or "Can I ..." (neng). You simple state "yī píng pí jiǔ" (一瓶啤酒) - literally: 'one bottle of beer'. It's short (because Chinese is efficient that way) and commanding (after all, you're the customer).
And if you wanted to be really polite (yet still speak like Chinese people speak), you could say "qǐng gěi wǒ yī píng pí jiǔ" (请给我一瓶啤酒) - 'please give me a bottle of beer'.
No questions asked.