The most common and most likely answer to this crossword clue is the 9 letter word CENTIPEDE
I've seen this crossword clue in The Guardian
C
E
N
T
I
P
E
D
E
More clues leading to the result CENTIPEDE
Buddy explains!
The straight part
We know that "Many members naturally support it" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case many members naturally support it = centipede.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 CENTIPEDE mean?
CENTIPEDE noun- Any arthropod of class Chilopoda, which have a segmented body with one pair of legs per segment and from about 20 to 300 legs in total.