The most common and most likely answer to this crossword clue is the 9 letter word POLYANDRY
I've seen this crossword clue in The Times
P
O
L
Y
A
N
D
R
Y
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The straight part
We know that "taking on several partners" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case taking on several partners = polyandry.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 POLYANDRY mean?
POLYANDRY noun- The having of a plurality of husbands at the same time; usually, the marriage of a woman to more than one man, or the practice of having several husbands, at the same time.
- The mating pattern whereby a female copulates with plural males.
- Sexual relations with multiple males, by a female or a male, human or non-human, within or without marriage.