Point 101 in MODALITY/adverbs is defined:

‘could’ + subject + ‘possibly’ to make requests more polite

**This is a very rare structure across corpora for a B1 structure. This point overlaps the more common and general: B1 questions with adverbs:*

Could you possibly tell me how to fix this?

An iWeb search for:

**. Could I|you possibly ***

1 . COULD YOU POSSIBLY TELL 34

2 . COULD YOU POSSIBLY GIVE 26

3 . COULD YOU POSSIBLY HELP 24

4 . COULD I POSSIBLY BE 20

5 . COULD YOU POSSIBLY MAKE 20

6 . COULD YOU POSSIBLY DO 16

7 . COULD YOU POSSIBLY EXPLAIN 15

8 . COULD I POSSIBLY HAVE 14

9 . COULD YOU POSSIBLY POST 13

10 . COULD YOU POSSIBLY SEND 13

Note that this form is not most common with requests:

*** Could _P possibly ***

1 . COULD IT POSSIBLY BE 192

2 HOW COULD IT POSSIBLY BE 153

3 HOW COULD YOU POSSIBLY KNOW 133

(what) 4 MORE COULD YOU POSSIBLY WANT 121

5 ? COULD IT POSSIBLY BE 85

6 WHAT COULD IT POSSIBLY BE 80

7 COULD IT POSSIBLY BE 79

8 HOW COULD I POSSIBLY BE 68

9 , COULD IT POSSIBLY BE 63

10 MORE COULD YOU POSSIBLY ASK 61

*There is not one example of this grammar in the PELIC or TLC.*