Diet design for vegetarian health is challenging due to the limited food repertoire of vegetarians. This challenge can be partially overcome by quantitative, data-driven approaches that utilise massive nutritional information collected for many different foods. Based on large-scale data of foods' nutrient compositions, the recent concept of nutritional fitness helps quantify a nutrient balance within each food with regard to satisfying daily nutritional requirements. Nutritional fitness offers prioritisation of recommended foods using the foods' occurrence in nutritionally adequate food combinations. Here, we systematically identify nutritionally recommendable foods for semi- to strict vegetarian diets through the computation of nutritional fitness. Along with commonly recommendable foods across different diets, our analysis reveals favourable foods specific to each diet, such as immature lima beans for a vegan diet as an amino acid and choline source, and mushrooms for ovo-lacto vegetarian and vegan diets as a vitamin D source. Furthermore, we find that selenium and other essential micronutrients can be subject to deficiency in plant-based diets, and suggest nutritionally-desirable dietary patterns. We extend our analysis to two hypothetical scenarios of highly personalised, plant-based methionine-restricted diets. Our nutrient-profiling approach may provide a useful guide for designing different types of personalised vegetarian diets.