Here is another angle on legitimism. (You may want to read that post to make sense of this, if you haven't already.)
Legitimism requires that if legitimacy is capable of bearing the burdens it lays on those whom it creates, it must. If God is infinite (very big, very fast, even if not truly infinite -- or even infinite, if infinity can be actual?), then he can experience all the experiences that any beings experience. And in fact, he should, simply in order to have metaphysical contact with all beings. (And in order to be able to speak the simantic word of "all things" to us.) So it is easy to see how he could literally bear the burden of each thing that occurs to any and all of his creatures. However, he could not experience what it was like to experience all these things and not simultaneously experience everything else that exists.
I don't want to take away from God's firsthand experience of what each person experiences. It is literally as intense as whatever each person experiences. It would have to be. God would have to experience the tunnel vision each of us experiences, where we only know what we know. That's what it means to experience literally the same experiences we experience. And yet he would experience the rest of his experiences as well.
By knowing the bigger picture, though he really would experience exactly what his creatures experienced, he would know more, and on some level that would enable him to have distance from their experiences that they don't have. He would really know enough of what was going on to be justified in making the laws of the universe (in the sense of knowing how everything relates to every other existing thing), and he would also be justified by having the disposition to bear our burdens to as great an extent as he could, but one could say that there is a missed opportunity, which he can't take, to be a creature and nothing but a creature.
If it is possible for God to share the formation of the laws of the universe with a finite being, then that being can live an ordinary human life, without the distance that comes from greater awareness, and that finite being could then play a part in upholding legitimacy. It would be by his will as well as God's that the laws of the universe were formed. The two would authoritatively assent to the laws, and thus give them their legitimacy, and thus they would both be God (in the legitimist sense, of the highest being, most worthy, most authoritative, deciders of the way things are, the single source of legitimacy, made up as it seems it must by more than one person). If it were possible for God to co-create with a finite being, he should, in order to enable there to be a member of legitimacy who could experience the finite element of creaturely life. Since he can, and should, he did.
However, now we come to the question, how many finite lives must be lived by the finite co-creating member of God (the Son)? Will the Son live every human's life? Or just one? The argument for just one could be that for the sake of justice, the Son could only die once. As a member of legitimacy, the Son does no injustice and does not deserve death, but could die for others' injustices. Having paid for them once, he couldn't die again, since he would be paying for nothing, and thus there would be no redeeming value for the extra injustice of each further death he experienced. This is something that fits into biblical Christianity, and I want to support that option (as I have begun to in this post on the Atonement.)
However, I think it's possible that the story given above, which would limit the number of deaths that the Son could undergo, could possibly not be true. I think if someone "entered the MSLN path" from a secular beginning, they might not see justice and Atonement as necessarily following from the founding principles of MSLN. So legitimism could be seen as having a more, and less, biblical interpretation. The less biblical one might find some other limit to the number of deaths that Jesus would undergo, but I can't think of one right now. So instead I will try to account for how the Son could experience the lives of each person (or animal, assuming as is reasonable that they are "minds" in a Berkeleian sense, or even in some sense "personal beings"), as a finite being with as little extra context beyond what each creature experiences in their life, for as many creatures as possible.
The Son could share subjectivity with the stream of consciousness that is identical to that of a creature, unable to do anything to affect what happens in it. It would be like watching a movie, in total detail (or even more so, entering an experience machine). He would do this for each of the billions of creatures that have ever lived or ever will live. Because the Son is finite, he would experience each one in order, one after another. This process would take a finite amount of time, and might be compressed. So the Son might experience them all in a second of the "master clock", even if it took him billions of years in his subjective time. In this way, he would be able to bear the burden of all beings.
(13 June 2021, update: I think it unlikely now that there could be a real difference in rates of subjective experience. So I would say that it really may take Jesus billions of years to go through all those lives, not compressed into one second. Perhaps all other beings would sleep and not notice the passage of the billions of years, when only the Father and Son would be awake.)
In order for him to still be himself while experiencing this, he would still have to add something to his experience of the creature while he experienced it. There is no substitute for being yourself and nothing more. But he need not be aware of the full range of knowledge normally available to him. When he is experiencing what an atheist experiences, he might be an atheist, or doubt the existence of God to as great a degree as possible for him, due to the perspective of the atheist, which does not trust the appearances of God in life. He might not know anything more than what they know, from birth, besides whatever bare amount is necessary for the Son to be the Son. So he could bear our burdens in a finite though still not identical way, and, given the requirements of legitimacy to have the maximal willingness to bear the burdens of those under its rule, he should and thus does.
But it is possible that you could say that the Son doesn't really die if all he's doing is "watching movies". Perhaps if he lives his own life on earth, and no one else's, then he can be fully immersed in that life and experience death the same way we do. But when he shares a life, he may always find some distance from the shared life, as when we watch even the most immersive movies, the distance which enables him to remain being himself as he "watches".
In that case, if the Atonement only limits his deaths to one, he could still "co-live" multiple lives. He could know the finite lives of each being (and would, for the sake of legitimacy), to the greatest extent possible, and thus would experience all of our lives. This makes fairly literal what Jesus says when he says "what you do to the least of these, you do to me".
In the case where we assume the Atonement and justice do not obtain such that the Son's deaths are limited to one, then how many times would the Son have to die in order to bear our burdens? He would have to experience his own life and death by himself, to understand that aspect of human experience. There is something unique in human experience of living your own life and no one else's. He would also experience each of our unique ways of living and experiencing death. Would the Son need to keep living lives and dying by himself? He would have already experienced all the uniqueness of our lives and deaths (by having co-lived them as described above). But would he have to experience them for himself, without being separate from our consciousness? Maybe. Perhaps the Son lives and dies lives, by himself, which are similar to every other human life, so as to experience all of them, for and by himself. I think (for now) as long as the number of these lives are finite, I don't see a problem with affirming this.
We could say that each simantic word (of the extraordinary, but finite, number of possible simantic words), which humans experience in their lives, mostly have already been experienced by the Son and the Father as they "coined" them before bringing humans into consciousness. But to whatever extent they attain a new meaning, and to whatever extent they can be experienced as a single human in a limited lifetime, the Son could experience each word as such.
One problem, though, is that if the simantic words have not been modified until after humans live their lives, then the Son would not be able to live them until after those lives were over. But many lives will continue forever, and presumably simantic words will keep evolving or being refined for all eternity. The Son can't bear the burden of all of our existences.
However, one could argue that the burden of legitimacy is different from the freedom of it. The burden will all be lifted when all sin is gone. The way things should be is liberation for those in tune with trustworthiness, who can therefore trust. (Trust and trustworthiness are liberation.) The way things should be is a burden when it demands that we change or that we pay a price, because we are out of tune with trustworthiness.
In any case, if it is impossible for the Son to not bear a burden, then he does not have to. Legitimacy arises (at least, this is a necessary condition) from the disposition, as far as is possible, to bear the burdens you levy on others when you make a law.