Plato espoused equality in nature between men and women, but not for just deserts with regards to human rights... for the benefit of society:
Regarding eugenics: it is quite clear to me that Plato was advocating a eugenics-like virtue in using the structure of government to attempt to make the next generation better through selective human reproduction, but that he was not about to attempt to overthrow monogamy among his guardian class. Read this:
[Equality with regard to work and sport], then, is one difficulty in our law about women, which we may say that we have now escaped; the wave has not swallowed us up alive for enacting that the guardians of either sex should have all their pursuits in common; to the utility and also to the possibility of this arrangement the consistency of the argument with itself bears
Yes, that was a mighty wave which you have escaped. Yes, I said, but a greater is coming; you will of this when you see the next.
Go on; let me see.
*The law, I said, which is the sequel of this and of all that has preceded, is to the following effect, --'that the wives of our guardians are to be common, and their children are to be common, and no parent is to know his own child, nor any child his parent.' *
Yes, he said, that is a much greater wave than the other; and the possibility as well as the utility of such a law are far more questionable.
I do not think, I said, that there can be any dispute about the very great utility of having wives and children in common; the possibility is quite another matter, and will be very much disputed.
I think that a good many doubts may be raised about both.
You imply that the two questions must be combined, I replied. Now I meant that you should admit the utility; and in this way, as I thought; I should escape from one of them, and then there would remain only the possibility.
But that little attempt is detected, and therefore you will please to give a defence of both.
Well, I said, I submit to my fate. Yet grant me a little favour: let me feast my mind with the dream as day dreamers are in the habit of feasting themselves when they are walking alone; for before they have discovered any means of effecting their wishes --that is a matter which never troubles them --they would rather not tire themselves by thinking about possibilities; but assuming that what they desire is already granted to them, they proceed with their plan, and delight in detailing what they mean to do when their wish has come true --that is a way which they have of not doing much good to a capacity which was never good for much. Now I myself am beginning to lose heart,
and I should like, with your permission, to pass over the question of possibility at present. Assuming therefore the possibility of *the proposal, [of abolishing marriage among the guardians] * I shall now proceed to enquire how the rulers will carry out these arrangements, and I shall demonstrate that our plan, if executed, will be of the greatest benefit to the State and to the guardians. First of all, then, if you have no objection, I will endeavour with your help to consider the advantages of the measure; and hereafter the question of possibility.
I have no objection; proceed.
First, I think that if our rulers and their auxiliaries are to be worthy of the name which they bear, there must be willingness to obey in the one and the power of command in the other; the guardians must themselves obey the laws, and they must also imitate the spirit of them in any details which are entrusted to their care.
That is right, he said.
You, I said, who are their legislator, having selected the men, will now select the women and give them to them; --they must be as far as possible of like natures with them; and they must live in common houses and meet at common meals, None of them will have anything specially his or her own; they will be together, and will be brought up together, and will associate at gymnastic exercises. And so they will be drawn by a necessity of their natures to have intercourse with each other--necessity is not too strong a word, I think?
Yes, he said; --necessity, not geometrical, but another sort of necessity which lovers know, and which is far more convincing and constraining to the mass of mankind.
True, I said; and this, Glaucon, like all the rest, must proceed after an orderly fashion; in a city of the blessed, licentiousness is an unholy thing which the rulers will forbid.
Yes, he said, and it ought not to be permitted.
Then clearly the next thing will be to make matrimony sacred in the highest degree, and what is most beneficial will be deemed sacred?
And how can marriages be made most beneficial? --that is a question which I put to you, because I see in your house dogs for hunting, and of the nobler sort of birds not a few. Now, I beseech you, do tell me, have you ever attended to their pairing and breeding?
In what particulars?
Why, in the first place, although they are all of a good sort, are not some better than others?
And do you breed from them all indifferently, or do you take care
to breed from the best only?
From the best.
And do you take the oldest or the youngest, or only those of ripe
I choose only those of ripe age.
And if care was not taken in the breeding, your dogs and birds would greatly deteriorate?
And the same of horses and animals in general?
Good heavens! my dear friend, I said, what consummate skill will our rulers need if the same principle holds of the human species!
Certainly, the same principle holds; but why does this involve any particular skill?
Because, I said, our rulers will often have to practise upon the body corporate with medicines. Now you know that when patients do not require medicines, but have only to be put under a regimen, the inferior sort of practitioner is deemed to be good enough; but when medicine has to be given, then the doctor should be more of a man.
That is quite true, he said; but to what are you alluding?
I mean, I replied, that our rulers will find a considerable dose of falsehood and deceit necessary for the good of their subjects: we were saying that the use of all these things regarded as medicines might be of advantage.
And we were very right.
And this lawful use of them seems likely to be often needed in the regulations of marriages and births.
Why, I said, the principle has been already laid down that the best of either sex should be united with the best as often, and the inferior with the inferior, as seldom as possible; and that they should rear the offspring of the one sort of union, but not of the other, if the flock is to be maintained in first-rate condition. Now these goings on must be a secret which the rulers only know, or there will be a further danger of our herd, as the guardians may be termed, breaking out into rebellion.
Had we not better appoint certain festivals at which we will bring together the brides and bridegrooms, and sacrifices will be offered and suitable hymeneal songs composed by our poets: the number of weddings is a matter which must be left to the discretion of the rulers, whose aim will be to preserve the average of population? There are many other things which they will have to consider, such as the effects of wars and diseases and any similar agencies, in order as far as this is possible to prevent the State from becoming either too large or too small.
Certainly, he replied.
We shall have to invent some ingenious kind of lots which the less worthy may draw on each occasion of our bringing them together, and then they will accuse their own ill-luck and not the rulers.
http://classics.mit.edu/Plato/republic.6.v.html, emphasis added
My esteemed collaborators here on philosophy.stackexchange have said that the above-quoted rules and principles upholding marriage were not meant for the guardian class. I can't find this principle defended anywhere in the text, though. The mechanism by which children would not be known to be related to their parents was a scheme of common infant-rearing, not the natural outcome of multiple sexual partners.
That marriage was specific to individuals was also affirmed by the patriarchy rule that children born to two individuals not paired by the by the ruler should not be reared. (461b)
Also, the thought that the wives of the guardians would be "common", as quoted by others here on philosophy.stackexchange, is treated in the Republic as a proposal which may have either utility or possibility, or both... and its possibility was at first called paradoxical and eventually denied... and in case of any further argument, that section of the Republic closes with this: