The most common and most likely answer to this crossword clue is the 5 plus 5 letter word SPLIT LEVEL
I've seen this crossword clue in The Guardian
S
P
L
I
T
L
E
V
E
L
More clues leading to the result SPLIT LEVEL
Buddy explains!
The straight part
We know that "Stagger inside" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case stagger inside = split level.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 SPLIT LEVEL mean?
SPLIT LEVEL noun- A building of this kind.
- Of a building: built with rooms on levels separated by stairs of less than a full storey.