Mezuzot on Both Doorposts?

Question: I am unsure to which doorpost to affix a mezuza. May I affix one on both sides, or is that prohibited as bal tosif (adding on to amitzva)?
Answer: We will start with some of the basic rules/opinions of bal tosif. Tosafot (Rosh Hashana 16b) asks how we can blow shofar both before and during Musaf without violating bal tosif and answers that there is nobal tosif on repeating a mitzva more times than necessary. The Rashba (Rosh Hashana 16a) says that one does not violate bal tosif if the additional activity is mandated by Chazal. (The Rambam (Mamrim 2:9) says that if the Rabbis formulate their Rabbinic law as if it is a Torah obligation, they are in violation of bal tosif.)
Many Acharonim compare the matter of two mezuzot due to a doubt to that of two sets of tefillin due to a doubt, and the latter is the subject of much discussion. The Shulchan Aruch (Orach Chayim 34:2) says that one who wants to don the "tefillin of Rabbeinu Tam" in addition to "the tefillin of Rashi" should, if possible, don both pairs at the same time. The Shulchan Aruch just requires avoiding bal tosif by having in mind that while whatever is really the correct tefillin is for the mitzva, the other one is "no more than straps." (Tosafot Yeshanim, Yoma 57a says that adding to a mitzva just for the purpose of eliminating doubt is not subject to bal tosif, but this is not the accepted opinion.) The Tur (OC 34) rejects the relevance of bal tosif more fundamentally, saying that it applies, for example, when one has five compartments in the tefillin, but not by wearing two separate pairs of normal tefillin.
Many take issue with the Tur based on a gemara in Eiruvin (96a), which says that one who finds tefillin on Shabbat outside an eiruv and wants to wear them so that he can bring them to safety may not wear two pairs at a time, among other reasons, because of bal tosif. While we cannot summarize all the discussion on the matter, we mention that the Magen Avraham (34:2) says that one can don two pairs of tefillin only if one of them is not kosher. The Mishna Berura (34:8) says that the Shulchan Aruch’s case is permitted only because it has two factors that minimize bal tosif: 1. the extra element is separate from the basic one (see Sanhedrin 88b); 2. one of the entities is unfit for the mitzva. Even then, one should intend that only one of them (we do not know which) is for the mitzva.
Along the lines of the gemara, the Pitchei Teshuva (Yoreh Deah 291:2) says that one who puts two mezuzot on the same doorpost violates bal tosif. This is not as strange an occurrence as one might think. Poskim discuss, for example, one who rents an apartment from a Jew who is not very careful about mitzvot who has a tiny mezuza case covered by paint, which the renter does not have permission to remove. Then, the question is whether he can affix another one.
Regarding your question of putting mezuzot on two posts, where only one can be obligated in a mezuza, Acharonim disagree. The Binyan Tzion (99) says that the mezuza that is on the wrong door post has no more halachic significance than the wrong pair of tefillin, and therefore the Shulchan Aruch’s idea of donning two pair of tefillin can be applied to mezuzot on the two questionable posts. The Maharam Shick (Yoreh Deah 287) argues that a kosher mezuza affixed to a door post, even when it is to the doorpost that does not have an obligation, falls within the realm of the mitzva, making it subject to bal tosif when it is opposite a mezuza in the right place.
Among contemporary poskim, while there is no clear consensus (see Yabia Omer VI, OC 2), the stronger opinion is to not sanctionmezuzot on opposite door posts, whether as a clear ruling (Minchat Yitzchak I:9) or as a practical preference (Shevet Halevi III:150; Bemareh Habazak (IX:35). In addition to formalistic bal tosif issues, it is problematic policy to create a an odd-looking new phenomenon of twomezuzot, even if it is out of a desire for stringency/covering all bases, which itself is very often a two-edged sword.