Crossword Genius

On which to stand a drink, perhaps (3)

Ross

I believe the answer is:

mat

I'm a little stuck... Click here to teach me more about this clue!

'drink perhaps' is the definition.
Although both the answer and definition are singular nouns, I can't understand how they can define each other.

'on which to stand a' is the wordplay.
I cannot quite see how this works, but
'on' could be 'at' (I've seen this in other clues) and 'at' is located in the answer.
A single letter 'm' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for mat that I've seen before include "dull finish" , "Thick flat pad on the floor" , "Paint with a dull surface" , "Small carpet" , "Shoe-cleaner" .)

I've seen this clue in the Evening Standard.
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