That is what is called polyandry, and often (but not always, oddly enough) is paired to a matriarchal society.
There are still some examples today of such society in Tibet where several distinct groups organized in that way. It's what you would call "classic polyandry"
In this system the land is rather scarce so society evolved following the most logical path of having several men working one plot rather than trying to find one property each. Often in these societies one woman is married to 2 or more men that are all brothers (the men are related to each other, not to the woman). This allows the owned land to remain within one family undivided as these societies are not matrilineal (matrilineal = property passes from mother to daughter)
Another reason that moved some societies towards polyandry was a matter of protecting the household while the husband was away. With multiple husbands there would have always been someone present (Eskimo, Inupiaq, Iglulik, Alutiq and Inuit were an example of this)
As arrangement, polyandry was widely used: South-american tribes used it (Bari, Yanomamamo, Cubeo, Aymara, Panoan Matis, Cashinaua, Guaja, Zo'e, Suri, Kaingang, Ache and others), North-american Natives used it (Aleuts, Comanche, Tlingit, Shoshoni, Cherokee, Blackfoot, Pomo, Utes, Innu, Pavitoso and Pawnees are just some of the most notable examples cited in literature, according to researchers many more have been reported but overlooked in the past), Arctic populations used it (as mentioned) was common in Asia and Africa and it's not completely disappeared yet, researchers say that there are at least 80 different societes in the modern world that still practice it in one way or the other. In Sri Lanka for example this is recognized under Kandyan marriage law. Even in Europe, ancient Germans and Britons were some tribes that researchers mention as practicing some form of polyandry.
A paper by Katherine E. Starkweather and Raymond Hames "A Survey of Non-Classical Polyandry" not only shows how it was a practice more common that what was thought but also gives an explanation on why it was thought that way (from here):
So how is it that, in spite of all this evidence of polyandry
accumulating steadily in the literature, anthropologists for so long
passed along the "it's virtually non-existent" story? Starkweather and
Hames suggest anthropology has been accidentally playing a scholarly
version of the Telephone Game.
In 1957, George Murdock defined polyandry in a seminal text as "unions
of one woman with two or more husbands where these [types of union]
are culturally favored and involve residential as well as sexual
cohabitation." Using such a strict definition, Murdock could
accurately say polyandry was extremely rare; almost no cultures have
polyandry as the dominant and most preferred form of family life.
Then subsequent scholars mis-repeated Murdock's remark; polyandry went
from being understood as "rarely culturally favored" to "rarely
permitted." Thus mating diversity that was known to exist became
relatively invisible in the big story told by anthropology about human
mating. (If you write off every exception to a supposed rule, you will
never think to challenge the rule.)
In an email interview with me, Starkweather remarked, "I don't think
that anyone, including Murdock, was operating from an explicitly
sexist standpoint. However, I do think that the definitions of
polyandry, and thus perceptions about its rarity, may have been due at
least in part to the fact that an overwhelming percentage of
anthropologists collecting data and shaping theory at the time were
men." During Murdock's time, "there seemed to be a fairly pervasive
belief that polyandry didn't make any sense from a male's
Polyandry does not mean that women are the head of the household, in many cases you find that is the eldest husband the one that takes decisions. Matriarchal societies (= headed by females) on the other hand do not imply that there is polyandry and matrilineal societies do not mean polyandry or matriarchy is included in the deal.
Nothing prevents you to put all three together and have a society where the women took the role men had in our more recent, and well known, western society. Despite having found quite some people online calling it the end of humankind its not at all impossible that the same environmental, cultural and religious situations that brought so many groups to practice matriarchy, matrilineality and polyandry cannot be put all together in an alternate world.
Some references for the above are (there are many more, it would be a long list, its long as it is and i wont bother formatting it as this isn't a school paper):
Johnson and Zhang ‘Matriarchy, polyandry, and fertility amongst the Mosuos in China’; Ellis ‘On Polyandry’; Levine and Silk ‘Sources of Instability in Polyandrous Marriages’; Smith ‘Is Tibetan Polyandry Adaptive? Methodological and metatheoretical Analyses’; Steward ‘Shoshoni Polyandry’; Starkweather ‘Exploration into Human Polyandry: An Evolutionary Examination of the Non-Classical Cases’; Starkweather and Hames ‘A Survey of Non-Classical Polyandry’; Berreman ‘Pahari Polyandry: A Comparison’; Cassidy and Lee, ‘The Study of Polyandry: A Critique and Synthesis’; Childs, ‘Polyandry and population growth in a historical Tibetan society’; McLennan 'Primitive Marriage: An Inquiry into the Origin of the Form of Capture in Marriage Ceremonies'