With regard to constant technological innovations in the bakery sector in order to increase bread nutritional value without affecting its technological and sensory characteristics, we applied pseudocereals/oilseeds to obtain an optimal formulation. A factorial design 33 was used and the independent factors were chia flour (levels: 0, 10, 20% flour basis), quinoa flour (levels: 0, 20, 40% flour basis), and amaranth flour (levels: 0, 20, 40% flour basis). Their effects and interactions were studied through the response surface methodology to optimise the bread formulation from a holistic viewpoint, which included the nutritional, technological and sensory characteristics. The optimum formulation with the highest quality was the blend made with 10, 4, and 20% of chia, quinoa, and amaranth, respectively. The results showed a significant increase in protein amount, ash, lipids, and crumb firmness compared to wheat bread. The calorie value of the control sample and the optimised formula were significantly similar, bearing in mind the high lipid amounts present in raw materials. Loaf-specific volume slightly decreased in comparison to control bread, as expected in formulations with gluten-free raw materials and a large amount of fibre. The optimised formula presented nutritionally/functionally higher indexes and similar overall acceptability to the control bread (p < 0.05).