1

This a line from "good morning call"

その横で平気な顔していられるか?

Next to that can you wear a cool face ?

How would one explain ~て いる in its potential form ~て いられる ?

I understand it as "Next to that can you be wearing a cool face ?"= so a nuance of ability/potential with emphasis on being a continuing action rather than say 顔できる [can wear a face] which is more declarative.

Am I correct ?

3

You are correct that していられる is the potential form of the している. However, you cannot replace it with できる. できる removes the progressive tense that している expresses. For example:

平気な顔ができる。
To be able to make a calm face.

Although maybe you could argue that with context, this sentence would mean something more natural, but it sounds like someone saying that they "can physically make a calm face."

平気な顔している。
Making a calm face.

平気な顔していられる。
To be able to keep making a calm face.

So, for your example, it would instead mean to "keep making a calm face" because it is the potential progressive form of the verb する. I'm guessing something very surprising or scary happened, so this sentence expresses "There's no way I/could maintain a calm expression."

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