Patriarchy versus Matriarchy, or is there an in-between grey area?

All of the subsequent argument would not be possible did not Queen Elizabeth the 1st challenge the patriarchal more.  Of course, in this patriarchal society of the Queen Elizabethan era (although maybe it tended to be less patriarchal with a Queen at the throne), women had dowries and men fought each other to wed the woman whom everyone desired.  In this case, Shakespeare employs this stereotype of how relationships are formed and turns it on its head and hangs it upside down.  Men were expected to sing love songs (Feste) while women would listen by attentively: Shakespeare again tells something different about the abilities of women to deceive and to work, and the meaning of attractiveness.  The only hope of women achieving intellectual success would be cross-dressing women, which Shakespeare has set-up in his play as an important motif.  

In modern times, men who cross-dress are often misconstrued as being homosexual, which has changed ever since the play days of Shakespeare.  Metrosexual is the closest term I know of to the idea of cross-dressing for men, short of actual cross-dressing that is with bras and other feminine attire:  

Another term that I can think of for women who are eager to reap the monetary privelages that men have solely enjoyed are women from the early 20th century who fought for the right to vote in America (it was earlier in England that women could vote), and women who fought for the abolishment of separate spheres in the military, workplace, or feminists who are still popular to this day:

In "Twelfth Night," Viola who cross-dressed as men--and not just any cross-dress--but in a really good, hollywood-esque, and convincing manner--could do any job that a man could do.  In terms of a matriarchal paradigm, which the play seems to exhibit, men were all turned into fools by the knave-like, deceitful Viola, and in a justly manner.  

A pun that the authors of the Norton English 2nd edition forgot to put in is Viola's name, which is the name of a stringed instrument.

I would argue that this play does not do enough to challenge the heteronormative, but rather, it places women still in a position of weakness compared to that of men.   Despite Orsino being increasingly fond of Cesario and then leaving all thoughts of being with Olivia behind him, he marries Viola and marriage seems to uplift her status whereas before, she had no high status.  In this patriarchal world, Viola's background as a parentless child suggests that only certain conditions can be set-up to create a character such as Viola, who is perhaps at war with society than at peace with it.  The only hope of transforming the heteronormative female gender role is only possible when the bastards of society are out to change it, it would seem.  I would argue yes, and it's for the better.  Sebastian, her brother, who was accused of stealing, also would be considered somewhat at odds with society, for conducting illegal, immoral activities, which go unaddressed.