'box after box' is a correct and usable part of a sentence in written English.
For example, you could write: "The shelves were filled with box after box of books."
"We had looked at box after box after box, and they seemed so uninteresting".
Salye's companion, whom she called her sister, fetched box after box of documents.
Much to the chagrin of collectors, Tim's archive consists of box after box of unsigned prints.
Hank's officers deliver box after box of data to his garage.
Mr. DiLillo shipped him box after box until he got the packaging right.
At home, he and his wife trudged to the attic where they emptied box after box, rifling through old papers.
But Mia's grandmother (Gretchen's mother-in-law) sends boxes after boxes of fabulously frilly pink dresses, tights and bows.
As he doodled I went through box and bin after box and bin like a five-year-old.
Most people come in on the east or west side on McGalliard Avenue and you just see box store after box store.
But as blue box after blue box containing votes was emptied in the main hall, and with each announcement devoid of shock, and confirming that Salmond's name wouldn't be carved alongside Wallace or Bruce just yet, talk in the Marriot was turning to the consequences of winning.
