The most common and most likely answer to this crossword clue is the 8 plus 4 letter word FOLLOWED SUIT
I've seen this crossword clue in The Times
F
O
L
L
O
W
E
D
S
U
I
T
Buddy explains!
The straight part
We know that "did likewise" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case did likewise = followed suit.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.