I think I've found the family on the 1915 NY State Census. Names / ages match up, as does year of arrival, and the fact that two of the children appear to be twins.
1915 census - 242 Broome St., Manhattan
None are naturalized.
Abram Stein, b. Russia, age 54
Gertie Stein, b. Russia, age 55
Sam & Bennie, age 21 (Schmere & Benze from manifest)
Oscar, age 19 (Chatzkel from manifest)
The manifest shows that their daughter, Leie Stein, (b. about 1892) naturalized in 1942. Leie may have been married by 1915.
Good luck in your search,