Combine starter, warm water, honey, rye flour, wheat germ, and 1 cup of the bread flour in the bowl of an electric stand mixer; stir with a wooden spoon until smooth. Cover; let stand at room temperature until surface is bubbly, about 4 hours.
Fit electric mixer with dough hook. With mixer running on low speed, gradually add 1 1/4 cups bread flour to starter mixture, and beat until combined after each addition. Add salt. Increase speed to medium-low, and beat until dough pulls away from sides of bowl, about 6 minutes, adding up to 1 cup additional flour as needed. Transfer dough to a lightly greased bowl. Turn dough to grease top. Cover with plastic wrap; let stand at room temperature until increased in volume, 1 1/2 hours.
Transfer dough to a lightly floured surface. Shape dough into 2 equal balls (about 12 ounces each). Cover with a clean kitchen towel, and let rise until puffy, about 45 minutes. Use immediately, or wrap in plastic wrap and store in refrigerator up to 24 hours. Let chilled dough come to room temperature before using, 45 minutes to 1 hour.