Subjects will progress through desensitization to a high maintenance dose - 1200 mg of crushed peanut, 200 ml of milk or 1200 mg of egg powder.

Subjects will progress through desensitization to a low maintenance dose - 120 mg of crushed peanut, 50 ml of milk or 300 mg of egg powder.

Subjects will begin desensitization with cooked versions of the allergen (muffins in the case of egg and milk) or transformed versions (Bamba puffs for peanut). They will progress up to a full muffin or 4 Bamba puffs (for egg/milk and peanut respectively). Once subjects have reached these doses, they will transition to doses of pure allergen. They will then progress to the same top dose as subjects in the High Dose Arm.

Participants consume increasing doses of allergenic food daily until they reach a maintenance dose. In the case of the High Dose Arm, participants will progress to a daily dose of either 1200 mg, 300 mg or 200 ml of egg, peanut or milk respectively.

Participants randomized to the Low Dose Arm also begin by consuming small amounts of the allergenic food, gradually increasing the daily dose. However, participants in this group only progress to 300 ml, 30 mg or 50 ml daily dose of egg, peanut or milk respectively.

The Cooked/Transformed Allergen Arm begins the desensitization with a cooked or transformed form of the allergen - muffins in the case of egg or milk, Bamba puffs in the case of peanut. Participants take increasing amounts of these products (one muffin for egg and milk and four Bamba puffs for peanut) then transition to egg, milk or peanut. Participants then continue their dose progression, getting to 1200 mg, 200 ml or 300 mg for egg, milk and peanut respectively.

Do participants in the different study arms experience similar rates of anaphylaxis during their participation in the study? Anaphylaxis is defined as an allergic reaction to the food the subject is allergic to, that involves symptoms in two of the following organ systems: skin, respitratory, gastro-enterologic or neurologic.The Consortium for Food Allergy Research (CoFAR) grading scale will be used for assessing severuty of allergic symptoms

Do participants in the three study arms experience similar levels of desensitization to their allergen? This will be assessed by a Double-Blind Placebo Controlled Oral Food Challenge (DBPCFC). Doses of allergen that elicit symptoms strong enough to end the challenge will be compared between the three groups. Symptom severity will be graded using the CoFAR grading scale.