The most common and most likely answer to this crossword clue is the 8 letter word ENTRESOL
I've seen this crossword clue in The Guardian
E
N
T
R
E
S
O
L
More clues leading to the result ENTRESOL
Buddy explains!

The straight part
We know that "mezzanine" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case mezzanine = entresol.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does ENTRESOL mean?
ENTRESOL noun- A mezzanine; an intermediate floor in a building, typically resembling a balcony. Most often used to refer to the floor immediately above the ground floor and below a higher floor.