English expressions "Top me up"

Top me up please!
Can you top me up? = refill my glass or cup with more drink. Fill to the top again.
Can I top you up?
A: “More coffee sir?”
B: “Sure, top me up. Thanks.”
“Thanks for the top up.”

top somebody up

 (especially British Englishto fill somebody’s glass or cup with something more to drinkCan I top you up?related noun top-up

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