OK... here goes:
If you define "major" as one designed for complete re-builds, the answer is ONE.
BN had one "back shop" (major overhauls) at W. Burlington, IA
Other diesel shops:
Northtown (Minn.-St. Paul)
Kansas City, MO
Livingston, MT (BN closed it in mid 80's ?)
I *think* this is a complete list (or near complete). Mind you, this does not include the numerous "minor repair" facilities that were scattered across the system. Hope this helps!