Stay with me, please (2,2,5)

I believe the answer is:

be my guest

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'please' is the definition.
(I've seen this before)

'stay with me' is the wordplay.
I cannot quite understand how this works, but
'stay' could be 'be' (stay can mean to continue to be a certain way) and 'be' is located in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for be my guest that I've seen before include "Do as you wish!" , "Help yourself!" , "Please do!" , "do stay with me" , "as 1 [HOTELIERS] might say" .)

I've seen this clue in The Daily Express.

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