Mix starter and water: In a large bowl, stir together the active sourdough starter, warm water, and sugar or honey until mostly dissolved.
Add flours and salt: Stir in whole wheat flour, bread flour, and salt until a shaggy dough forms, adding only enough bread flour to bring it together — you may not need it all.
Incorporate oil: Drizzle in olive oil and mix until mostly incorporated.
Knead the dough: Knead for 5 minutes until smooth and slightly tacky. Cover and rest 30 minutes.
Stretch and fold: Do 3 sets of stretch-and-folds, 30 minutes apart. For each set: stretch one side over the center, turn a quarter, repeat on all 4 sides. Cover between sets.
Bulk rise: Place the dough in a bowl, cover, and let it rise until increased by 30–50%, slightly puffy, with small bubbles (1–3 hours).
Divide and shape: Gently deflate the dough and divide into 8 equal pieces. Shape each into a smooth ball by tucking edges underneath.
Roll out: Flatten each ball with a rolling pin into a 6–8 inch circle, about ¼ inch thick. Place on a lightly floured surface or baking parchment, cover, and rest 20–30 minutes. Preheat oven to 475–500 °F (245–260 °C) with a baking stone or heavy tray inside for at least 30 minutes. (If your oven can’t reach this high, set it to the maximum temperature. Your pitas may take a little longer to bake.)
Bake: Using a pizza peel or the edge of the parchment, slide 2–3 pitas onto the hot stone or tray. Bake 3–5 minutes until fully puffed and lightly golden.
Keep soft: Remove from oven and immediately cover with a clean towel. Repeat with remaining pitas.