The most common and most likely answer to this crossword clue is the 11 letter word MULTISTOREY
I've seen this crossword clue in The Times
M
U
L
T
I
S
T
O
R
E
Y
More clues leading to the result MULTISTOREY
Buddy explains!

The straight part
We know that "on many levels" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on many levels = multistorey.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 MULTISTOREY mean?
MULTISTOREY noun- A building with more than one storey.
- A car park or parking garage with more than one storey.
- (of a building) Having more than one storey.