The most common and most likely answer to this crossword clue is the 4 plus 4 letter word HIGH RISE
I've seen this crossword clue in Independent
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Buddy explains!
The straight part
We know that "Having many American stories" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case having many american stories = high rise.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 HIGH RISE mean?
HIGH RISE noun- A tall building, one of many stories.
- (of clothing) Designed to sit high on, or above, the wearer's hips.