Kang Yatse II (6,250m) in Ladakh is a proper high-altitude climb but technically manageable for fit trekkers with some mountaineering basics. Takes about 10-12 days including acclimatization from Leh. You'll use crampons and ropes near the summit. Best attempted July-September. The views from the top across Ladakh's peaks are absolutely worth the effort. https://www.thinairexpedition.com/kang-yatse-2-peak-expedition/