The most common and most likely answer to this crossword clue is the 9 letter word HIGH-RISE
I've seen this crossword clue in The Times
H
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More clues leading to the result HIGH-RISE
Buddy explains!

The straight part
We know that "Like some tall buildings/much liked by fat cats?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like some tall buildings/much liked by fat cats? = 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.