The current entry in LEO
to push the envelope [tech.] alles herausholen
can have the designation [tech.] removed.
to push the envelope [ifml.] über die Stränge schlagen
should be omitted as they are not equivalent.
According to http://www.idiomsite.com/pushtheenvelope.htm
Push The Envelope
To go to the limit of known performance. This idiom originated with the aeroplane industry. The limits of a plane's performance were marked on a two-dimensional graph. The envelope is the area of the graph that indicates safe usage. In use since the late 70's.
über die Stränge / den Strang schlagen
means "leichtsinnig aus der gewohnten Norm ausbrechen"
and Duden gives "die Grenze des Üblichen und Erlaubten auf übermütige, forsche, unbekümmerte Weise überschreiten"
I do not know how one should translate "Über die Stränge schlagen" into English.
The sense seems to be conveyed by "Fools rush in where angels fear to tread".
The concise Oxford Duden gives "to kick over the traces" (not in LEO), but this sounds like a false friend to me. Collins Practical dictionary suggests "run riot" (also not in LEO) but this too seems inadequate.