I'm using my circumstances as an example.
I don't have a strong Bachelors (it's in Math this past year) nor three strong letters of recommendation. I am 25 years old in the USA and have not held a full time or part time job yet. I have one volunteer unpaid internship in Hospital Information Technology (mostly blue collar work).
I want to go to a good school in Computer Science to study machine learning, but do not think I can currently afford it nor get accepted. I want to learn some significant mathematic theory in addition to the courses/electives offered in a C.S. masters.
How do I decide from a perspective (either mine or an employer's) whether it is productive to pursue two Master's Degrees back to back?
I am considering starting a Master's in Applied Mathematics focused on Finance/Business at an international university in a year with very low or free tuition (a country like Germany, France, Belgium), even if I have to learn the language.
One year into the degree, I would apply for Computer Science programs in the USA and Canada to study Machine Learning with a focus on Data Science after graduating.
Pros I have read about: I would have the ability to work part time throughout both degrees to pay living expenses. I am currently debt free. I would have multiple opportunities for internships and research. The programming done for my research would be part of my portfolio if I make it test-driven and production quality. I would learn two important and related skills for Industry. I would have the opportunity to travel. I would be more likely to get a fellowship/scholarship or TA/RA position that waives tuition for the second masters. At the right school, I could try very hard to have a significant part of my second degree be a collaboration with a company / organization to work on an important real world problem in industry together.
Cons I have read about: If I don't plan it right, this could be unbelievably expensive. Employers would view me as over qualified for certain positions. Employers may view me as a professional student and see red flags. It may look like I failed/dropped out of a PhD program. I would enter the job market significantly later than my peers (30 years old) causing red flags. I can only spend $40,000-60,000 USD total for both degrees, excluding living expenses, over the four years. Some employers may think that I will only be happy in a job that uses both of my specializations and I will get bored / move-on otherwise.
How do I figure out what employers value, and how do I decide what I value from these pros/cons?
How does one determine pros/cons they have over looked? I assume it is worth it to ask hiring managers on LinkedIn how they view the situations and credentials one would have in this scenario?
Edited in from answer by OP
What I decided to do was do the applied mathematics Master Degree with a focus on Business and Finance then pursue the PhD in CS.
The cons are just too big and give too big of an opportunity cost.