The most common and most likely answer to this crossword clue is the 11 letter word PROLIFERATE
I've seen this crossword clue in The Daily Telegraph
P
R
O
L
I
F
E
R
A
T
E
More clues leading to the result PROLIFERATE
Buddy explains!

The straight part
We know that "Breed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case breed = proliferate.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 PROLIFERATE mean?
PROLIFERATE verb- To increase in number or spread rapidly; to multiply.