One's altogether united in disguising dirty habits (8,4)

I believe the answer is:

birthday suit

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'one's altogether' is the definition.
'birthday suit' can be an answer for 'altogether' ('birthday suit' can be a synonym of 'altogether'). I am unsure of the 'one's' bit.

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for birthday suit that I've seen before include "State of total nakedness" , "Invisible attire?" , "Nothing to wear?" , "Invisible threads?" , "State of being unclothed" .)

I've seen this clue in The Telegraph.

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