This is a spin-off from Move an existing Stack Exchange account to a new user account?.
This feature request is to allow a collection of tech and non-tech Stack Exchange accounts that exist inside one user account to be split up among two user accounts.
There could be three categories that every Stack Exchange is assigned to, "tech", "non-tech" and "exceptional cases":
Inside these categories: moving an SE account to another user account should not be possible, as it is the rule of now. This is in order to a mess of SE account shifts.
Across these categories: if a user starts a non-tech Stack Exchange account in her "user account No. 1" and later realises that she would like to have it assigned to another user, this should be possible as long as the non-tech SE account that shall be moved to her "user account No. 2" does not belong to the tech category covered by her "user account No. 1". The whole thing applies the other way round as well.
Partly across these categories: there could be exceptions beyond such broad categories (e.g. tech didactics can account for both tech and non-tech, and in this case, it is allowed to shift the SE account in both directions). There should be very few exceptions (<10% of the Stack Exchanges) that allow this.
Added discussion of the main feedback up to now:
Since the comment discussion does not seem to work. I will go through every detail of the discussion points, and I think that your remarks are mainly not valid for this feature request, or there is an easy fix for them.
This feature request is to allow splitting up a collection of thematically different Stack Exchange accounts among multiple user accounts.
First off, why limit the feature request only to 'thematically different accounts'? The easiest way to allow this would be ... to allow this for any and all site profiles, regardless of their theme. Each site has its own theme already, which determines what is on- and off topic on such a site.
Invalid remark, as I explicitly ask for splits only among broad categories, it is clear that I mean those broad categories when I say "thematically different". This is essential to the whole feature request and also influences any discussion points that you make afterwards. I also do not know why you did not just delete this part when you knew that it is an invalid point, as we discussed in the comments.
Making categories is easy, but arguing that the sites in these categories are similar or different enough to make splitting off a profile okay or forbidden is not. Someone that wants to split off their profile on the arduino site because it's just a hobby from their Stack Overflow profile and put them under two different accounts would be barred from doing so, as both are grouped as 'technology'.
The categories do not have to be perfect science. The mere thing to distinguish something techy like drones and something obviously non-techy like "English Language and Usage" is obvious. This feature request is not to discuss the details anyway, it is about the main idea of being able to split up broad-category-wise.
While it does sound nice to be able to split off a profile instead of hide things, it's likely to cause more trouble than create benefits that can't be had already by using the feature to hide site profiles or creating a second account. So I'm going to say allowing users to do this is a very bad idea.
Invalid statement. This request shall see the hide-option not even as a workaround, instead, hiding should simply not count at all. It is good to mention it, but it should not be put against this request. Hiding will not serve as what this feature request is for. In the end, what is asked for is what most of the users seem to do anyway: having different accounts for different needs - without hiding anything. And the only difference here is that a user should be able to do this split later, when that decision has not been made early enough for some reason; all of this in clear borders of very few broad categories. Take just the two "tech" / "non-tech" categories if the exception case irritates too much.
Allowing people to just move site profiles between accounts would likely be a cause of many messes and open up new ways of abuse. As a quick example: If people can transfer one site profile to a sock, they can e.g. earn the association bonus for that sock account. And voilà: now the sock can participate in a sockpuppet ring and upvote posts, without ever having to even try and gain the first few reputation points. Without any restrictions, you could even move one site profile from sock, to sock, to sock, to sock....
One could also ask why the same user who has obviously proved that he can manage Stack Exchange should be forced to earn the first reputation points at all to comment and flag when opening up a second profile. And as to the association bonus, just suppress the effect of that association bonus as soon as it comes from such a moved SE account. That is all you need to weaken this point.
Networkwide suspensions could become useless. Keeping track of notorious troublemakers and trolls becomes harder. Is there anyone that wants to buy an SO account with a bit of rep and a good question, that allows you to flag and comment but won't get question banned as easily? I've got a PayPal...
You can configure any such move request so that any ban is taken with it. Moreover, you can only do a one-directed move by this feature request, that is, for example, moving a "non-tech" SE account (which belongs to the minority in your user account then, while "tech" is the majority of the SE accounts) to another user (perhaps even only a new one only, point of discussion), and not the other way round afterwards. It is a move with a ratched effect, no way back. The same would account for a "non-tech" being the majority, then you could only move the "tech" accounts.
The big mess?
The big mess is when an account can be moved again and again. Which is not impossible if you open up five empty tech SE accounts and then move the non-tech account further again, but what is the use of that if the ban would be taken with it and moved points will not have an effect of the other SE accounts? And you could also prevent some abuse by just counting those SE accounts that have passed some threshold of points.
In case you see a mess when too many people split up their SE accounts with this feature, this is no point either, since they could split up to as many users as they want anyway: if they decide so at the start.