I've found in most bread recipes, you can replace up to 1/4 of the flour with another flour without problematic effects on the dough. Some recipes may allow a higher level of replacement, and of course it matters what you're replacing the white flour with. White whole wheat flour is very similar to white flour, but things like flaxseed flour are not, and the more similar, the more you can replace.
In some cases, such as replacing white flour with cornmeal, semolina, or rye flour, it will strongly affect the flavor of the finished loaf. But you should be able to follow the same instructions for kneading, rising times, shaping and baking as the original recipe. Some grains affect the amount of water required for the recipe, though (buckwheat and cornmeal are especially absorptive).
I've done this many times, with a variety of different recipes (batard, focaccia, sandwich bread, pizza dough, etc.).