The main difference between using “may I” or “can I” is formality. Both are completely acceptable to use in the English language. However, “may I” demonstrates sophistication of character with a command of etiquette. In casual situations with friends or other social situations, “can I” is best.
It used to be there was a marked difference between the speech and word choice of an educated individual versus someone without it. The use of “can I” or “may I” was a definite speech distinction to denote refinement. But, people relaxed this subtle difference in recent decades. So, use “may I” when addressing someone in a professional situation or with someone who has seniority (age, experience, status etc).
The Meaning of “May I” and “Can I”
“Can I” and “may I” carry the same meaning: it’s a way of requesting an endorsement or permission to undertake an action. These often begin with a question inquiring about the allowance from another person. The word that follows “I” in this context will always be a verb.
The Formal: “May I”
To show respect to elders, display a command of language finesse or to be official in speech or writing, you use “may I.” No one really knows where it comes from or how this formality distinction began, but it’s a solid conformity in the English language as it stems from Britain.
May I take this moment to congratulate you on your achievements?
Grandmother, may I have another biscuit?
May I discuss our current state of affairs?
The Casual: “Can I”
“Can I” is best for informal situations that are casual and social with friends, cousins, siblings or others with whom you are familiar. You use it in the exact same manner as “may I.”
Can I take this moment to congratulate you on your achievements?
Sally, can I have another biscuit?
Can I discuss our current state of affairs?
“May I” or “Can I” in the Negative
When framing the negative, you will use “not” after “I” before the verb.
Grandmother, may I not have another biscuit?
Can I not discuss our current state of affairs?
The main takeaway here is how formal “may I” and “can I” are. Although both are acceptable to use, “may I” has a more polite ring that “can I” lacks, situation depending. Just remember that a verb comes after “I.”