With 'Stage photography' I think about difficult lighting, dark situations, etc. So a large aperture is required.
Is the f2.8 of the 24-70 satisfactory for you? Then maybe the 16-35 f2.8 II is a good option
If the max aperture is not sufficient, check out a prime, e.g. 17mm, 24mm, etc.
As these will cost some money, you could maybe rent them first to try them out ...