‘May have’ and ‘May have been’ indicate possibility
He may have left by now.
You may have forgotten your dairy on the table.
I may have have meant something else.
You may have left the window open.
The door may have been left open by mistake.
We may have been late by ten minutes.
The thief may have been arrested by the police.
The medicine may have been outdated.
Might have, Might have been
He might have gone to sleep.
They might have sold off their car.
She might have told you lies.
The bird might have died.
He might have been a thief.
She might have been angry at my mail.
You might have been unaware of her intentions.
She might have been drugged.
It might have been a holiday last Saturday.