Any child with multiple allergies unfortunately is going to have difficulties using an OTC pre-made weight gain product - especially whe milk allergy is an issue.

I would suggest making smoothies in a NEW blender than hasn't touched any allergens. For protien, there are many powders on the market, the simpler the better - avoid whey & if the child can use soy, that might be the ticket. I'd try to stick to VERY simple foods until you are sure of the child's allergies.

Has this young person reacted to eggs, wheat, corn, soy? Is he/she on a gluten-free diet?

It is very difficult to give a clear answer without knowing all the allergies involved, although I'd suspect a gluten-free diet wold be helpful, it may not be necesssary. It seems you need to define the allergies, even if the list is very long, more clearly to give a better answer. Also, you may need to look at probiotics to balance flora in the digestive tract (what you buy off the shelf generally will be insufficient to adequately treat someone with candida or other overgrowth problems.

Long story short, it seems you need to work with a dietician, naturopath, allergist, immunologist &/or possibly an endocrinologist to get to the bottom of why a child has so many allergies.

I would VERY strongly suggest getting this child off ALL processed foods & avoiding the allergens altogether to give the body time to heal, get rebalanced, etc. I am NOT a fan of forcing allergens on a child or even an adult, even in small quantities to "desensitize" them, and would avoid any practitioner that follows that train of thought, as it can be damaging in the long run, causing more sensitivities & more health problems when this person gets older.