"largely stemmed from" is a correct and usable phrase in written English.
It is typically used to describe the main or primary source or cause of something. Here is an example: "The decline in the company's profits largely stemmed from their failure to adapt to changing market trends." In this sentence, "largely stemmed from" is used to explain the main reason for the decline in profits.
These abject-yet-inorganic basslines largely stemmed from a single music-making program, Massive.
Both sides cited the proverbial philosophical differences that largely stemmed from the club's acquisition of several veteran Europeans who bristled under the direction of an American coach.
That largely stemmed from a sudden slowdown in property investment, growth in which slowed to 6% year-on-year, less than half the average pace of 14% in 2014.
Realizing that his defeat at Chocim (Khotin, Ukraine) in 1621 largely stemmed from the lack of discipline and the degeneracy of the Janissary corps, he proceeded to discipline them by cutting their pay and closing their coffee shops.
As the stock market roared forward on the heels of a historic bull market, the dominant view was that the good times largely stemmed from Mr. Greenspan's steady hand at the Fed.
The gains have largely stemmed from Macquarie's effectiveness as an operator, bringing in budget airlines, reconfiguring for the Airbus A380 (more traffic) and moving stores to behind the security barriers where (post-9/11) people can shop for longer because of early check-ins.
Particularly large European emigrant communities of Croats exist in Germany, Austria and Switzerland, which largely stem from the 1960s and 1970s migrations.
The problems largely stem from the airlines' efforts to improve their on-time records.
In fact, it largely stems from the fact that she's poor.
This change largely stems from the actions of the established developed nations.
The economic improvement in recent months largely stems from businesses cutting inventories at a slower pace.
