Dissolve yeast and sugar in warm water in a large bowl; let stand 5 minutes. Lightly spoon flour into dry measuring cups; level with a knife. Add 2 1/4 cups all-purpose flour, whole-wheat flour, oil, and salt to yeast mixture, stirring until well-blended. Turn dough out onto a floured surface. Knead until smooth and elastic (about 10 minutes); add enough of remaining flour, 1 tablespoon at a time, to prevent dough from sticking to hands (dough will feel tacky).
Place dough in a large bowl coated with cooking spray, turning to coat top. Cover and let rise in a warm place (85°), free from drafts, 45 minutes or until doubled in size. (Press two fingers into dough. If indentation remains, the dough has risen enough.) Punch dough down; cover and let rest 5 minutes. Divide dough in half; roll each half into a 12-inch circle on a floured surface. Top and bake according to recipe directions.
Note: This dough may be frozen. Follow directions for kneading dough, and shape dough into 2 balls. Coat balls with cooking spray and place into a ziptop plastic freezer bag. Thaw overnight in a refrigerator. Cover and let rise in a warm place (85'), free from drafts' 1 1/2 hours or until doubled in size. (Press two fingers into dough. If Indentation remains, the dough has risen enough.) Shape as instructed.