The following small side effects may occur:

Laxative effect: large uses of magnesium stearate could lead to a laxative effect. (8) Magnesium stearate may be a source of magnesium for constipation. Magnesium citrate and magnesium oxide are common magnesium forms for constipation.
Allergy may occur. A 28 years old woman affected by an allergic reaction from magnesium stearate with an urticarial manifestation. (9)
Diarrhea: excessive magnesium intake from magnesium salts for pharmacological/medicinal purposes may also cause diarrhea and other gastrointestinal effects.

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