I do not believe you want to be doing that!
This post was inspired by a recently-published study by Alan Aragon & Brad Schoenfeld, as bodybuilders are a group of people who often eat a rigid diet (some eat skinless chicken breasts, broccoli & brown rice for several meals each day).
See Nutrient timing revisited: is there a post-exercise anabolic window?
"Collectively, these data indicate an increased potential for dietary flexibility while maintaining the pursuit of optimal timing."
This post is also aimed at people who eat severely restricted diets in the (often mistaken) belief that something's making them ill.
People with type 1 diabetes who struggle to keep their blood glucose within reasonable limits (3 to 8mmol/L, or 24 to 144mg/dL) benefit from restricting their intake of high-GL carbohydrates, so this post is not aimed at them. See The problem with Diabetes.
People with type 2 diabetes who severely restrict their intake of carbohydrates must be in caloric deficit, otherwise the physiological insulin resistance caused by high serum NEFAs will mess up just about everything in their body if they are in caloric balance or caloric excess. I've read (so it could be false) that a certain non-skinny blogger who I'm in conflict with (who has type 2 diabetes and who eats a VLC diet) has heart problems and is taking medication(s) for high blood pressure. Hmmm.
People who suffer from gastrointestinal problems after eating gluten-containing foods, or mucus after eating casein-containing foods may have impaired gut integrity. See Gluten - more than just a pain in the guts?
Supplements that I consider of positive value are:-
Fish oils: If the diet is low in oily fish (tinned tuna is not an oily fish), there may be insufficient EPA & DHA (especially in men, children & post-menopausal women). Women of reproductive age can get away with taking flaxseed oil.
Magnesium: If the diet is low in veg/high in dairy, there may be too much Calcium relative to Magnesium.
Vitamin D3: If the lifestyle results in sun-avoidance, insufficiency in Vitamin D is highly likely.
Vitamin K2: If the diet is low in animal fats and/or fermented foods, insufficiency in Vitamin K2 is highly likely.
Supplements that I consider of negative value are:-
Vitamin A: If there's an insufficiency in Vitamin D, supplementing with Vitamin A/β-carotene may exacerbate it. As Vitamin D + Calcium may reduce cancer risk, supplementing with Vitamin A absent Vitamin D3 may increase cancer risk.
Vitamin E: If there's an insufficiency in γ-tocopherol, supplementing with α-tocopherol may exacerbate it. As γ-tocopherol may reduce CHD mortality risk, supplementing with α-tocopherol absent γ-tocopherol may increase CHD mortality risk. Most Vitamin E supplements contain α-tocopherol only. Some Vitamin E supplements contain mixed tocopherols and these are O.K.