"Would it be possible" grammar?

PooyanWould it be possible to assign me supervising a class taking place before Nov 20th?

assign me supervising is not correct.

Would it be possible to be assigned to the supervision of a class that meets before November 20?

CJ

How do we deduct the notion of "I need to be assigned" from your sentence and not He or She?

PooyanHow do we deduce the notion of "I need to be assigned"

It is deduced from the person asking the question. In other words 'for me' is understood if I am asking.

Would it be possible (for me) to be assigned ...

CJ

Can I use the same sentence If I mean that someone else needs to be assigned ?

PooyanCan I use the same sentence If I mean that someone else needs to be assigned ?

No. You'll have to include the for-phrase if you want that.

Would it be possible for [him / her / them / Henry / Susan / Mr. Smith] to be assigned ...?

You can only omit the for-phrase when it's for me.

CJ

Thanks, your comment was very helpful.

one more question. Are these sentences both correct?

"Would it be possible (for you) to assign me to a class . . . "
"Would it be possible (for you) to assign to me a class . . . "

Pooyan-
1 "Would it be possible (for you) to assign me to a class . . . "
2 "Would it be possible (for you) to assign to me a class . . . "

1 is good.
2 is not good. Drop the second 'to'.

Would it be possible (for you) to assign me a class ...

So it's one of these:

... to assign me a class
... to assign me to a class

As you said : You can only omit the for-phrase when it's 'for me'.

So the both following phrases convey the same meaning, right?

(A) : Would it be possible to arrange another time later in the week?
(a) : Would it be possible for me to arrange another time later in the week?

(B) : Would it be possible to push our meeting back to 3:00?
(b) : Would

yes, it is possible