Do you support the legalisation of polyagmy and polyandry

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Such relationships are rather base and primitive. There is a reason why marriage has changed it's context from being polygamous to monogamous.
Only the most primitive societies on earth still have polygamy as an institution. But sure, if you want to go back the same road of regression while claiming this a human rights issue, go ahead, friends.

I get that you consider it base and primitive, but what are your arguments against it (assuming you have any besides your religion saying so)? What, exactly, are the problems with multi-partner marriages? I'm honestly interested if you are aware of any actual flaws with the institution, since it's an area where I'm almost entirely ignorant.

I do have arguments against it ranging from equality within marriage, to the advantages of monogamous relationships.
Obviously, multi-partner marriges are focal points of confusion and instability for societies in which these were not practiced traditionally.
Even in my society, where polygamy was traditionally practiced, people now regard it as a very base practice. Reasons are these:

1-How is a single person going to include fairness into this relationship? Say, I have a wife, and she gets old, and I take up a new, younger wife. I suddenly stop showing attention to my old wife and start sleeping with my new one all week long.
Obviously, the point of such marriages are nothing but the animalistic suppression of carnal desires, and have nothing to do with commitment.

2-The children that are born from different mothers will obviously be in great confusion regarding the world around them, especially in places where monogamy has been traditionally practiced.

3-Another obvious flaw is that such marriages tend to be emotionally abusive towards the partners who are amongst the multitude. Like I said, many marriages break apart due to a side claiming that he/she is not shown enough attention by his/her partner, how is a marriage based on a single-multiple partnership going to survive other than by force?
Only in primitive societies where women are seen as belongings, this type of marriage is still prevalent, and these are generally women who have been forced into accepting a second or more wives, to share their men with.
How is this going to work on the basis of "mutual consent"? Obviously, one or multiple partners will have to suffer emotional abuse if such a "marriage" is to be continued, for I really wonder how many people are willing to share their men, or women. But they would have to cope with it if they are forced into it, yes? That is it. Polygamy rests on the shoulders of inequality and abuse. It has been so for many years.