After you correct your diet you must then use your judgment whether any experimental supplementation is necessary. For example, in the cases of Manganese and Selenium (in some parts of the world), it is easy with food alone to get to levels of these nutrients which, in supplements, would be considered dangerously high. Always use caution with supplementation of the minerals and the fat-soluble vitamins (A, D, E, K), because the body pools of these substances change only very slowly, and you may be unable to recognize any difference until toxicity begins. Vitamins A (retinol), D3, and K2 all have to be present in the body for each of these vitamins to work right. Vitamin K2 is the animal version of Vitamin K and the conversion from vegetable-sourced K1 to K2 can be very poor for humans. The USDA tables have very little data on Vitamin K2, only for some foods and only for menaquinone-4. For Vitamin D, the Daily Value equals about 20 seconds of sun exposure and is not an adequate allowance in the absence of sufficient sun exposure. The Daily Value for Vitamin A in international units (IU) vastly overstates the rate of conversion from vegetable-sourced carotenoids to real Vitamin A (retinol), so that you can be deceived into thinking everything is OK when it isn't. Especially if you eat ketogenically, you need retinol, not more beta-carotene.
The Daily Value for Sodium is a suggested upper limit with no scientific basis and is not a minimum daily requirement. Although NUT does not mention it, be aware that you need reliable sources of Iodine, such as seafood and iodized salt. Choline is a conditionally essential nutrient that is not mentioned in the Daily Value and is likely to be too low in the diet because the misguided advice to avoid dietary cholesterol leads one to avoid the best Choline sources, which are liver and egg yolks. Biotin, a B vitamin definitely in egg yolks, is difficult to assay in foods because although it is in many foods, it is often bound in such a way so that we cannot absorb it.
The Daily Value limits on Saturated Fat have no scientific basis and will be found to be counter-productive to vitamin and mineral intake in several ways, such as limiting the intestinal absorption of minerals and fat-soluble vitamins, increasing the Omega-6 to Omega-3 ratio, and reducing vital nutrients only obtainable from animal foods.
With the water-soluble vitamins, the "B"s and C, the experiments are much easier because these nutrients are in a constant daily flux, and a single substantial dose can frequently tell you within a day whether anything beneficial is happening. Vitamin B-6 is reported to cause irreparable nerve damage in large doses, but usually you need only a few times the Daily Value to make an informed judgment whether supplementation is useful. When one is not deficient, supplementation can cause unwanted effects, such as headaches or jumpy feelings from B vitamins, or the weirdest effect that I saw in my experiments: excessive Vitamin B-6 supplementation always made me dream of feces, apparently because B-6 is the characteristic intestinal signature of voluminous bacteria. I advocate that you buy all the B vitamins in individual supplements and apply the foolproof test: Take one right before bed when you do not have to be well-rested the following day. Those B vitamins that make you toss and turn and keep waking you up during the night are those B vitamins that you are probably not deficient in. The B vitamins that feel pleasant, give you a restful sleep, or appear to do absolutely nothing are the B vitamins which are your main candidates when a symptom shows up and you don't know which nutrient is missing. The one exception is B-12, which I would test during the day because it affects consciousness if you are deficient. And yes, you will end up with a zillion bottles of vitamins where you decided you didn't need it. But you will also have an invaluable mental picture of all of them that you can sort through to immediately determine the most likely candidate when something is wrong.
Don't take vitamin and mineral supplements unless you can see they are doing something and you can see what they are doing--then find the minimum amount of the supplement that accomplishes the task. Whenever I made a major change to my diet I always dropped all the supplements and made them prove their utility once again. The idea that you cannot know in the present that you are deficient in a vitamin or mineral is just a marketing ploy and guarantees that almost everything you take will be a placebo. Taking supplements as "insurance" doesn't insure you against anything because you don't know what you need, and if they left the nutrient you need out of the pill, you wouldn't know enough to be able to tell. But precise supplementation of exactly what you need makes a huge difference. And get a pill splitter--sometimes the whole tablet is just too much!