Whisk 4½ cups of bread flour with Bread Booster. Preheat oven to 400°F. Prepare a baking sheet lined with parchment paper or lightly oiled.

In a large mixing bowl, add 2½ cups of the flour mixture, sugar, undissolved yeast, and salt. Heat water and butter until very warm (120° to 130°F). Gradually add to flour mixture. Beat 2 minutes at medium speed of electric mixer, scraping bowl occasionally. Add 1 cup of flour mixture and eggs; beat 2 minutes at high speed, scraping bowl occasionally. Divide batter into equal amounts (about 1-1/4 cups) into 3 bowls.

Using ? of the batter, add the remaining flour mixture, use more flour if needed, 1 tablespoon at a time, to make a soft dough. Knead on a lightly floured surface until smooth and elastic, about 8 to 10 minutes. Cover; set aside.

For the next 1/3 of batter, add 1 tablespoon of oil, 2 tablespoons molasses, and enough whole wheat flour to make a soft dough. Knead on a lightly floured surface until smooth, slightly sticky and elastic, about 8 to 10 minutes. Cover; set aside.

Add remaining 2 tablespoons of oil, 2 tablespoons molasses, caraway seed, cocoa, and enough rye flour to the remaining 1/3 of batter to make a soft dough. Knead on a lightly floured surface until smooth, slightly sticky and elastic, about 8 to 10 minutes.

Divide each of 3 doughs into 2 equal portions; roll each piece into a 9-inch rope. Braid a whole wheat, rye, and white rope together, crossing loosely over each other only a few times; pinch ends to seal. Place on prepared baking sheet. Repeat with remaining dough ropes. Brush loaves with 1 tablespoon of olive oil. Loosely cover with plastic wrap and a tea towel; let rise in warm, draft-free place until doubled in size, about 20 minutes.

Place loaves in the oven and lower temperature to 375°F, bake for 30 to 35 minutes or until rich golden brown in colour and internal temperature reaches 190°F. Remove from baking sheet; cool on wire rack.