An equally valid question may be Can a Man love two women? With the given circumstances and environment that we are brought up in, the belief and value system imbibed into us and the subconscious that has been built into us for generations; the first thought that comes to mind is - What a blasphemy!
Let alone answering it; to understand this very complex question we have go back to the origin of the notion of monogamy - the practice of one man keeping only one wife or an women keeping only one husband. The human race was polygamous at the beginning as there was no concept of family or home. Do not be taken aback thinking about the stories of Adam and Eve; these stories were invented much later. As human beings started to have family and home, polygamy continued to prevail. Women were considered similar to cattle or wealth - men tend to accumulate them. Women also had liberty to engage in sex with more than one man of their choice. That of course later started to result in fights between men in an attempt to establish ownership.
The notion of monogamy was possibly invented to keep the human race away from fighting and killing each other over sex and thereby preventing the human race from becoming extinct. There was another more possible scientific reason of preserving the gene. Polygamy was threatening to weaken and degenerate genes as man and woman both were practicing sex with many partners mixing up all kinds of genes in the process.
So it was necessary to form a rule as to who can have sex with whom. It was also necessary to limit partnerships between two people so that there is a clear formula of forwarding the genes.
In times, this notion was included in some religion and thus got deeply rooted in our psyche and we have started to have only one partner. This also got embedded in our value system - the system which tells us what is good and what is bad. So, we started to believe that even if we like two women (or a woman like two men), that is not morally correct and we should restrict our thought and ourselves.
But that limited us only in the physical sense, the mind is much more powerful. In course of time mind grew stronger to overcome the taboos of the value system to be independent. The mind has been evolving constantly as we progressed socially. Even a few decades ago, thinking about other women or men was taken as moral disgrace. However, over the past few decades we have progressed socially to a level where we think that we are liberated. Many liberated men and women of today are out of the influence of the subconscious and dare to express their love for more than one man or women and choose more than one partner. I think there is nothing wrong to it.
So, loving more than one person was possible always, irrespective of whether sex is one of the ingredient of love or not. (otherwise how can a mother love all her children? Or how can you love all your friends?) Nobody will raise an eyebrow when we talk about loving more than one person when sex is not involved. We tend to hesitate thinking about loving more than one person only when that love eventually is likely to end up in sex. Why love has to be restricted to only one person when sex is involved and in all other cases nobody raises a question when you love more than one?