Two Mezuzahs on the Doorpost — Is It Bal Tosif?

I was required to sign a rental contract stating that I may not touch the mezuzahs, and since for several consecutive nights I have felt that the mezuzah needs to be checked, I am looking for a solution. May I place an additional mezuzah of my own next to the mezuzah that is already there, of course on the same doorpost?
Is there a prohibition of bal tosif, or is there no concern for bal tosif?

Shalom u’vrachah 

This involves the prohibition of bal tosif. 

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