If someone can't afford to go to school for an MBA, but wants to train to be a manager, is there some compatible Master's, which has a reasonable level of support (teaching assistantships)?
I would definitely suggest the Chartered Financial Analyst program (aka, the CFA exam, https://www.cfainstitute.org/pages/index.aspx) for learning the few "hard" skills I would expect a business manager to have - such as, accounting, basic finance, elementary quantitative/organizational skills, etc.
Not only is it basically free compared to the cost of an MBA - total cost = $4000 is possible - it is, with regard to the relevant, real, demonstrable skills and knowledge base, far more rigorous and comprehensive than probably any MBA program (explanation below).
While I am not exactly sure what you mean by "a reasonable level of support (teaching assistantships)", if interpreted as "a desire to obtain requisite knowledge", I believe this is the best route available regardless of how much money you have. If that interpretation is incorrect, then hopefully the following will help out a bit.
While the CFA program is considered to be a graduate level program, it is not an actual university "Master's". This may be of concern when considering the culture of management and, more generally, business today.
First of all, you can get an MBA in about 2 years. Furthermore, you can do so while applying very little effort. Of course this all depends on the school, whereas the CFA takes at least 4, if you make it through. (Last I saw, success rates for the level 1 exam were 33% - has there ever been an MBA program that failed 2/3's of their freshmen class in any given year? Levels 2 and 3 have rates slightly higher, somewhere around 45-50%)
Combined with the notion that university education, especially in these related fields, has been transformed almost completely into an instrument for class division and social hierarchy (and away from learning and education), it may be (and I am certain it is) that an MBA is not for training, knowledge, skills, performance, etc, etc. but rather as a prerequisite for acceptance into the management/business class/social structure.
For evidence of this see the growth in the administrative body of universities compared to faculty and combined with absurd growth in the costs of it and ask yourself what this does to the society at large and why it is necessary. Not satisfied? Need a stat?
According to the article by Andy Beckett in a recent Guardian publication, "In 2017, half of recent UK graduates were officially classified as “working in a non-graduate role.”
Combine those tidbits with the fact that evaluating the success, merit or performance of managers, or of the tatics/skills/curriculum generally associated with their education is extremely difficult if not impossible. And the idea that what you are really paying for with an MBA is the acceptance into a social class may at least seem plausible.
Now, it is apparent that I am not a fan of the whole business world and the state of higher education but, I think it is hard to argue that the value in the MBA program is not, at least in some material way, dependent on what it means for one's social status. And this value must be accounted for when accessing the CFA program which is void of such factors.
Another commonly referred to source of business school value is that of "networking". I'd love to trash that idea as it is literally the opposite of what university education purports to be (pursuit of knowledge, anyone?) but, it does in fact hold some value somehow, and that source of value is absent from the CFA.
And, in demonstrating evidence for my claims against b-school and management and to back up the idea that we cant even be sure if any of it or its teachings have any value or truth at all, don't forget that the business/MBA led world recently failed to predict, understand, or even recognize the complete collapse of the system they were suppose to understand and were completely in charge of.
If you can ignore the emotions such a statement and its content may invoke and realize that my goal is to compare the program I suggested as an answer to your question, then it should be evident that while the points I have made may be debatable, hold some amount of truth. Because of this and that I don't think I fully understand what you are looking for, I think these points are relevant when considering alternatives.
Anyways, this got long, point is, if you are seeking to learn management principles you would be fine in buying maybe a couple hundred bucks worth of books. This is essentially the CFA is combined with a difficult exam to validate yourself with. Whatever the case, best of luck.
 https://www.theguardian.com/news/2018/jan/19/post-work-the-radical-idea-of-a-world-without-jobs  Full disclosure,I passed the first 2 levels of the exam before focussing on software development. But I can attest the fact that it is pretty difficult but definitely achievable.