Nevertheless desirous of obtaining a monopoly? (5,3)

I believe the answer is:

after all

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'nevertheless' is the definition.
(after all can mean nevertheless)

I don't understand the remainder of the clue.

(Other definitions for after all that I've seen before include "In spite of everything" , "In spite of any indications to the contrary" , "Taking everything into account" , "When everything is said and done" , "comes in last?" .)

I've seen this clue in The Globe and Mail.

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