Modals do not occur in the imperative. They don't have infinitive forms, which the imperative uses.

• Real imperatives: Leave at once. Go out the back door. Be quiet.
• Ungrammatical imperatives: *May leave at once. *Can go out the back door. *Could be quiet.

However, various phrases with modals have become common as indirect impositives.
In the examples below, the bald on-record challenge shut up sounds incongruous framed
with such indirect fripperies, designed to distract from public face loss by the addressee.
This is to emphasize that it's the modal in the construction that implicates the order or request/
("Impositive" is the cover term for both orders and requests -- they're both impositions):

• Would you mind waiting a moment/shutting up?
• Do you think you could possibly wait a moment/shut up?
• Can you wait a moment/shut up for a minute, my love?
• You could possibly wait a moment/shut up, you know.
• It would be OK if you waited a moment/shut up now.

If one substitutes a neutral verb like wait, the result is a possibly peeved but certainly courteous request. Not a bald immperative like shut up. These are conversational implicatures of the sort discussed by Gordon and Lakoff.

Modals do not occur in the imperative. They don't have infinitive forms, which the imperative uses.

• Real imperatives: Leave at once. Go out the back door. Be quiet.
• Ungrammatical imperatives: *May leave at once. *Can go out the back door. *Could be quiet.

However, various phrases with modals have become common as indirect impositives.
In the examples below, the bald on-record challenge shut up sounds incongruous framed
with such indirect fripperies, designed to distract from public face loss by the addressee.
This is to emphasize that it's the modal in the construction that implicates the order or request/
("Impositive" is the cover term for both orders and requests -- they're both impositions):

• Would you mind waiting a moment/shutting up?
• Do you think you could possibly wait a moment/shut up?
• Can you wait a moment/shut up for a minute, my love?
• You could possibly wait a moment/shut up, you know.
• It would be OK if you waited a moment/shut up now.

If one substitutes a neutral verb like wait, the result is a possibly peeved but certainly courteous request. Not a bald imperative like shut up. These are conversational implicatures of the sort discussed by Gordon and Lakoff.