push the envelope

push the envelope AND stretch the envelope (challenge yourself, innovate, take risks; to go beyond the limit of what has usually been done or was the accepted standard) — раздвигать рамки привычного или дозволенного; выходить за привычные рамки; расширять границы привычного, традиционного, дозволенного; рискнуть сделать что-то новое и необычное; ~ найти нетрадиционное, оригинальное решение ...

Example 1: Our methods are not working. We need different, innovative ideas — we need to push the envelope.

Example 2: They pushed the envelope of good taste by showing a naked fat man in their new ad campaign.

Example 3: Song titles are notorious for pushing the envelope on grammar. (chaika)

Example 4: Well, we'd like to illustrate absurdity by being absurd. We, on this show, like to push the envelope. We like to get close to that line and occasionally cross over that line.

push the limits (attempt to exceed the existing limits; try to do things beyond normal (or usual, or familiar, or acceptable) standards) — перейти границы дозволенного, выходить за рамки дозволенного, привычного и т. д.; зайти слишком далеко

Example 1: TV shows are really pushing the envelope / pushing the limits by showing so much sex and violence.

Example 2: Mud wrestling on TV was once considered pushing the limits, but now it is commonplace.

Example 3: Food manufacturers and marketers are pushing the limits of what is considered truth and what is considered a simple technicality.The countless food advertising tricks that are used to persuade us to buy their products are out of control.

see also
[think outside the box]

(exceed the limits of what is considered proper behavior)
cross the line
go too far
overstep the mark

exceed the limits of propriety
(go beyond what is considered decent behavior)