In the English Grammar Profile, B1 point 77 in MODALITY/adjectives is defined:
‘if-‘ clauses + ‘possible’, as a politeness strategy.
The examples in the EVP show that this might even be A1:
A1
Is it possible to speak to the manager, please?
Please send it today, if possible.
Is it possible to buy tickets in advance?
Cambridge Learner Corpus Learner example:
If possible, I would like to eat lasagne, because I love Italian food.
An iWeb search for:
If * * possible
1 IF AT ALL POSSIBLE 13144
2 IF IT IS POSSIBLE 9513
3 IF IT ‘S POSSIBLE 6148
4 IF IT WAS POSSIBLE 3506
5 IF IT WERE POSSIBLE 3128
6 IF THIS IS POSSIBLE 2710
7 IF THAT ‘S POSSIBLE 1657
8 IF THAT IS POSSIBLE 1563
9 IF THAT WERE POSSIBLE 540
10 IF THAT’S NOT POSSIBLE 539
11 IF THAT WAS POSSIBLE 400
12 IF IT BE POSSIBLE 372
13 IF IT’S EVEN POSSIBLE 321
14 IF IT’S NOT POSSIBLE 291
15 IF THAT’S EVEN POSSIBLE 284
16 IF THIS WAS POSSIBLE 262
If possible * * *
*we removed end of sentence.
1 IF POSSIBLE, TRY TO 1138
7 IF POSSIBLE, YOU SHOULD 538
9 IF POSSIBLE, I WOULD 421
10 IF POSSIBLE, IT IS 372
11 IF POSSIBLE, USE A 328
*The examples of this form in the TLC have nothing to do with politeness.