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Keeper of everything, with increasing difficulty, keeping nothing (7)

Ross

I believe the answer is:

hoarder

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'keeper' is the definition.
(someone who hoards or keeps hold of things)

I can't explain the remainder of the clue.

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(Other definitions for hoarder that I've seen before include "One saves" , "One with hidden store" , "Accumulator" , "Collector" , "Person unlikely to throw things away" .)

I've seen this clue in The Times.
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