One possibility that has no example in our past (that I know of) is a division of power/labor.
Simple put, women look after the soul and men look after the body.
There is a nurturing and life giving Goddess with her priestesses. They take care of all things supernatural and have (on the surface, at least) authority over all worship related events.
The men are responsible for the protection and expansion of the society. They rule, war, enforce laws, etc.
For this to actually work, several aspects of the society have to be "just right." That's because eventually people will end up in power who want power and are loathe to share that power.
So, how do we stabilize this situation.
First, have it ingrained from childhood that the role of men is to take care of women and that women are the source of wisdom. Boys are trained to fight and women are taught how to read and write. This only works for the common classes though. Higher classes and those who are sociopaths won't care.
Second, make a man's status depend not on what he owns but how well taken care of the women in his family are. If you wife walks around in a frock and your daughters are hungry, you are (or soon will be) at the lowest rung of society. This helps control the higher classes since to gain or maintain power, they have to show that they are worthy.
Third, the women have to have have a monopoly on the knowledge of the society. Most religions got started because the priests/priestesses held some necessary knowledge like when to plant or when the Nile would flood. So, within the women's circle, an individual's contribution to the health (mental and physical) of the society would determine her status. Their stratification could be along the lines of academia. The more knowledge they know and share, the higher their status. Figuring out a way of breeding better wheat jumps your status over several levels, etc.
This society has the chance to be stable.
It also lends itself to some interesting counter culture characters with which you can explore the boundaries of the society.
The girl who wants to fight. The boy who wants to read.
The girl who just wants to wear frilly dresses and knit all day. The boy who wants to gather wealth for himself.
The woman who enjoys tearing people down, giving purposely bad advice, and making their lives miserable. The man who rapes or beats women.