Due to the effect of climate change, wheat flour qualities with extremely high dough extensibility or dough strength are becoming more common, which impairs the production of selected wheat products such as pastries. The aim of this study was to investigate the effect of sorghum, millet, amaranth, or buckwheat addition to such a strong gluten common wheat flour (Triticum aestivum) on its rheological and baking properties. Raw materials were analyzed chemically (ash, protein, fat, starch, total dietary fiber) and physically (water absorption index, water solubility index, and pasting properties). Selected rheological analyses (Farinograph® and Extensograph®) were carried out on wheat blends, including up to 30% alternative grains. The baking properties of the blends were evaluated on standard bread and sweet milk bread recipes. Results showed that low amounts (5%) of sorghum and millet improved the dough stability of the high-gluten wheat flour. For optimum dough extensibility, additions of 30% sorghum, 15% millet, or 20% amaranth were needed. The use of gluten-free grains increased bread volume and decreased crumb firmness of the sweet milk breads when added at lower levels (5–15%, depending on the grain). In conclusion, cereal blending is a supportive tool to mitigate the effects of ongoing climate change and can enhance biodiversity and nutrition.