In Goethe's Faust, how do both Faust and Gretchen each express an attempt to exceed the limits of social norms and expectations that surround them?...

Let us base the answer to this question entirely on their relationship, specifically, the disparate nature of their origins, the goals that they both have in mind, and how everything ends.

In Daniel Wilson's introductory analysis of Faust (Yale University Press version of 2014), Part One of Faust is much more effective than Part Two, particularly for the social commentary that it elicits. This social commentary comes in the form of the challenging of social norms that is evident in the relationship that Faust wants to start with Margaret. Being that she comes from such a different social status than Faust, we can already sense that the relationship will not turn out so well.

In order to understand exactly how Faust attempts to push the social norms with Margaret, we must know where she comes from and who she is.

In Goethe's Faust Part I Margaret, or Gretchen, is a very pious and innocent woman, and daughter. She is not perfect; she does enjoy the occasional attention of males, and she is aware of her beauty. Nevertheless, she is a woman of good and well-meaning intentions who expects to be married one day.

The problem with Gretchen is not so much her character, but that of the people who surround her. Part of the social commentary discussed by Wilson is the criticism of the "small town mentality".

This is the idea that small town people are equally small in intellect. Hence, those who live with, or around Gretchen, are quite unlikely characters. Her brother, Valentine, is brash and uncouth, her mother is money-hungry, and her best friend Marthe is quite mature in the ways of the world.

That woman seems to me expressly made
To play the pimp or ply a gipsy’s trade.

Still, Margaret is aware of her social limitations and she has an inkling that Faust may be way above her status. This is not to say that Margaret is poor, for she is not; however, she is in no way a sophisticated woman of the world, either.

I am, in truth, of humble blood—
The gentleman is far too good—
Nor gems nor trinkets are my own

How does she push her social limitations? 

She does this by accepting Faust as a potential lover, even knowing what could happen if she gets carried away. Gretchen does get carried away. She accepts gifts, and she even trusts him enough to accept a "sleeping potion" to keep her mother away from her room while she lets Faust in. The potion was actually poison, her mother dies, and Gretchen ends up pregnant with the child of this man, whom she hardly knows that well.  

Still, Gretchen does not demand marriage from Faust; not even love. She could be seen as a modern woman by the modern reader, in that she shows a clear understanding of what is at stake by being a single mother in her society. It is despair that leads her to kill the child (we know that the baby drowns, but we are not told how exactly it happened), and she is eventually sentenced to be hanged.

Therefore, Margaret allowed herself to take a risk in becoming involved with a man who was beyond her "station", and also took another risk in trusting him enough to allow him in her bed. All backfires on her, but God ends up forgiving her.

How Faust pushes his limits:

Faust is not a stupid man, by any means. He is a greedy, narcissistic and self-absorbed man, but not an unintelligent one. When Faust sees Gretchen for the first time, he is aware of her station, and he gets to see the pious side of her. He has been at a higher level his entire life, and knows what is at stake at trying to seduce a less worldly woman. Moreover, he knows that she is a woman of limits. He, of course, wants her to give in and break away from her standards. It is because Gretchen has a truly beautiful character, and is not just a pretty shell of a woman, that Faust starts to develop true and sincere feelings for her.

Unfortunately, even though Faust aggravates Mephistopheles by feeling more than just lust for Gretchen, Faust never really makes his wrongs into "rights". This means that he never really offers Gretchen any solid foundation to the romance that he wants to establish with her. He may have the capricious want to be with a woman of lesser station, but he does not show any indication of being serious enough to change his life for her.

All this being said, which of the two may be considered "successful" at breaking with the social norms?

Arguably, the big winner (as Part Two will anticlimactically show) will be Faust, himself. Leave aside the fact that he faces no consequences for decimating almost an entire family (Gretchen's), nor for ruining the poor woman, nor for never even bothering with the child he had with her... and not even for having sold his soul. After a number of moral deaths, Faust is just "let go" easily from his negotiation and, in an ending that had angered many readers, he gets to just continue to exist despite of everything.

Gretchen, unfortunately, may have shown signs of strength as a woman of her time undergoing terrible circumstances, but she ultimately suffered every consequence that Faust was spared.