In a large bowl, mix the yeast with the water and sugar and let stand until foamy, about 5 minutes. Stir in the salt, whole wheat flour and 1 tablespoon of olive oil. Gradually add 2 cups of the all-purpose flour, stirring with a wooden spoon until the dough is fairly stiff. Turn the dough out onto a well-floured work surface and knead, gradually adding as much of the remaining all-purpose flour as necessary, until it is smooth, elastic and no longer tacky, 5 to 6 minutes.
Transfer the dough to a lightly oiled bowl and brush the surface with olive oil. Cover the bowl with plastic wrap and let the dough rise in a warm, draft-free place until it doubles in bulk, 1 1/2 to 2 hours.
Punch down the dough and knead it lightly, then return it to the bowl. Cover the bowl and let the dough rise again until doubled in bulk, about 45 minutes. Punch down the dough again and use or refrigerate.
The Pizza Dough can be refrigerated overnight or frozen for up to 1 month. Let the dough return to room temperature before using.