Demand side interventions, such as dietary change, can significantly contribute towards the achievement of 2030 national sustainable development goals. However, most previous studies analysing the consequences of dietary change focus on a single dimension of sustainability (e.g., environment) using a limited number of indicators and dietary scenarios. A multi-dimension and multi-indicator analysis can identify the potential trade-offs. Here, starting from the current food consumption data (year 2011), we first designed nine alternative dietary scenarios (healthy Swiss diet, healthy global diet, vegetarian, vegan, pescatarian, flexitarian, protein-oriented and meat-oriented diets and a food greenhouse gas tax diet). Next we calculated three nutritional quality (nutrient balance score, disqualifying nutrient score, percent population with adequate nutrition), five environmental (greenhouse gas, water, land, nitrogen and phosphorus use), one economic (daily food expenditure) and one human health indicator (DALYs) for current and alternative diets. We found that transition towards a healthy diet following the guidelines of Swiss society of nutrition is the most sustainable option and is projected to result in 36% lesser environmental footprint, 33% lesser expenditure and 2.67% lower adverse health outcome (DALYs) compared with the current diet. On the other extreme, transition towards a meat or protein oriented diet can lead to large increases in diet related adverse health outcomes, environmental footprint, daily food expenditure and a reduction in intakes of essential nutrients (for Vitamin C, Fibre, Potassium and Calcium). We found that shifting to the vegetarian and vegan diet scenarios might lead to a reduction in intakes of certain micronutrients currently supplied primarily by animal-sourced foods (Vitamin B, Choline and Calcium). Results show that achieving a sustainable diet would entail a high reduction in the intake of meat and vegetable oils and a moderate reduction in cereals, roots and fish products and at the same time increased intake of legumes, nuts, seeds, fruits and vegetables. We identify several current data and research gaps that need to be filled in order to get more accurate results. Overall, our analysis underscores the need to consider multiple indicators while assessing the dietary sustainability and provides a template to conduct such studies in other countries and settings. Future efforts should focus on assessing the potential of different interventions and policies that can help transition the population from current to sustainable dietary patterns.