The most common and most likely answer to this crossword clue is the 12 letter word INTERRELATED
I've seen this crossword clue in The Times
I
N
T
E
R
R
E
L
A
T
E
D
Buddy explains!
The straight part
We know that "like parts of a conspiracy?" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case like parts of a conspiracy? = interrelated.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 INTERRELATED mean?
INTERRELATED adjective- Having a mutual or reciprocal relation or parallelism; correlative.