It's very common with 'would like':I know there's a tendency to reduplicate perfects meaninglessly in sentences like this; I can't for the life of me think why.
But they mean different things. Each is right in its place. Sometimes one's preference at some time in the past may differ from what - now - one would have preferred.
'I would have preferred to keep my cool, but I'm afraid I lost my temper.'
'I would prefer to have kept my cool; it would have been more adult.'
The distinction is slight, but sometimes I think it's worth making. ;-)