Looking up...
Il a enfilé un manteau par-dessus son pyjama.
He pulled a coat on over his pyjamas.
Above and across something, over the top.
Le chat a sauté par-dessus la clôture.
The cat jumped over the fence.
On top of, in addition to.
Et par-dessus tout, il a perdu ses clés.
And on top of everything, he lost his keys.
From par plus dessus, above.