Crossword Genius

One in support of drink, or flat on the floor? (3)

Ross

I believe the answer is:

mat

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'floor?' is the definition.
(thesaurus)

'one in support of drink or flat on the' is the wordplay.
I cannot quite see how this works, but
'one' could be 'a' (a thing is one thing) and 'a' is located in the answer.
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is located in the answer.
A single letter 'm' remains which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for mat that I've seen before include "Opening of good book" , "Rug; without a shine" , "Floor-pad" , "Shoe-cleaner" , "Unglossy floor pad" .)

I've seen this clue in the Evening Standard.
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