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Matzah related stringencies:
Matzah Ashira-Egg Matzah:
The Ashkenazi custom is not to eat Matzah Ashira during Pesach. See Chapter 8 Halacha 5 for the full details of this topic!
Machine made Matzah:
The Chabad custom is not to eat machine made Matzah at all throughout all the days of Pesach. See Chapter 8 Halacha 3 for the full details of this topic!
Not to eat Matzah past the first night of Pesach:
Some are scrupulous not to eat any Matzah throughout Pesach with exception to the first night, when it is a Biblical command, and when required for the Shabbos and Yom Tov meals. However, the Poskim argue against this custom saying it diminishes Simchas Yom Tov.
 Toras Menachem 5711 2:7; See Otzer Minhagei Chabad p. 29-31
 See Shaareiy Teshuvah end of 461:1; Otzer Minhagei Chabad p. 42 regarding Rav Itche Demasmid that he would bake 12 Matzahs for the entire duration of Pesach
 The reason: As they suspect the Matzah may not have been made properly and thus contains Chametz.
 Shaareiy Teshuvah ibid