Company A, a C-Corp, was formed as a shell, started a 401(k), and the one employee of A rolled over his 401(k) account balance from a former employer. The 401(k) then bought all of the stock of A, and A bought a fast-food franchise with the proceeds. Some years went by, business grew, and A (still wholly owned by the 401(k)) wants to adopt a DB plan for the benefit of all its employees.
Any reason this can't be done? It seems to me that A is run as any other business, and in fact already sponsors a qualified plan (the 401(k) plan that owns A), so I don't see any reason why not.
Would the answer be any different if the franchise were its own entity, and instead of owning it outright, A and the other entity were a controlled group?