I would like to approach this question in two ways

1. In Tractate Menachos 33a ואמר רב יהודה אמר שמואל כתבה על שני דפין פסולה מיתיבי כתבה על שני דפין והניחה בשני סיפין פסולה הא בסף אחד כשרה ראויה לשני סיפין קאמר And Rav Yehuda says that Shmuel says: If one wrote a mezuza on two sheets it is unfit. The Gemara raises an objection from a baraita that teaches: If one wrote a mezuza on two sheets and placed it on the two doorposts of the entrance, it is unfit. The Gemara states the objection: By inference, if the mezuza was affixed on one doorpost, it is fit, despite the fact that it is written on two sheets. The Gemara answers: The baraita is not referring to a case where one affixed the mezuza on two doorposts. Rather, the baraita is saying that if it was written on two sheets in such a manner that it is fit to be affixed to two doorposts, i.e., there is a space between the writing of the first and second passages, so that one can separate the two sheets for different doorposts, it is unfit. This is in accordance with the statement of Rav Yehuda, citing

Shulchan Aruch Y”D 288:1-2, כיצד כותבין את המזוזה כותבין שתי פרשיות שמע והיה אם שמוע על דף אחד ביריעה אחת ועושה לה ריוח מלמטה וריוח מלמעלה כמו חצי צפורן ובתחלתה ישייר כדי לגול אותה אחר שתכרך. (ובסופה אין צריך להניח כלל) (טור): ב צריך לכתבה בדף אחד ואם כתבה בב' או בג' דפין כשרה:

2. A nice chiddush that I read in the Sefer Vedibarta Bam quoting the עיטורי תורה quoting the Midrash Rabbah 18.3 in which Korach asked this question regarding a room filled with Sifrei Torah does it need a mezuzah? , he explains as follows. The slogan of the early reform movement in Germany was “be a true Jew at home, but on the outside be a person like everyone else” similarly korach said of the Jewish people “the entire community is Holy and g-d is among them (16:3). He meant that Jews were all Holy since they all had g-d in their hearts. He asserted, thus that its go to be a Jew on the inside without openly showing it on the outside. Moshe disagreed that one should manifests one’s Torah convictions in public to let the world know that the home is a Jewish one with a mezuzah. We all know how the turn of the events took place.

I would like to approach this question in two ways

1. In Tractate Menachos 33a ואמר רב יהודה אמר שמואל כתבה על שני דפין פסולה מיתיבי כתבה על שני דפין והניחה בשני סיפין פסולה הא בסף אחד כשרה ראויה לשני סיפין קאמר And Rav Yehuda says that Shmuel says: If one wrote a mezuza on two sheets it is unfit. The Gemara raises an objection from a baraita that teaches: If one wrote a mezuza on two sheets and placed it on the two doorposts of the entrance, it is unfit. The Gemara states the objection: By inference, if the mezuza was affixed on one doorpost, it is fit, despite the fact that it is written on two sheets. The Gemara answers: The baraita is not referring to a case where one affixed the mezuza on two doorposts. Rather, the baraita is saying that if it was written on two sheets in such a manner that it is fit to be affixed to two doorposts, i.e., there is a space between the writing of the first and second passages, so that one can separate the two sheets for different doorposts, it is unfit. This is in accordance with the statement of Rav Yehuda, citing

Shulchan Aruch Y”D 288:1-2, כיצד כותבין את המזוזה כותבין שתי פרשיות שמע והיה אם שמוע על דף אחד ביריעה אחת ועושה לה ריוח מלמטה וריוח מלמעלה כמו חצי צפורן ובתחלתה ישייר כדי לגול אותה אחר שתכרך. (ובסופה אין צריך להניח כלל) (טור): ב צריך לכתבה בדף אחד ואם כתבה בב' או בג' דפין כשרה:

2. A nice chiddush that I read in the Sefer Vedibarta Bam quoting the עיטורי תורה quoting the Midrash Rabbah 18.3 in which Korach asked this question regarding a room filled with Sifrei Torah does it need a mezuzah?