The impact of extreme events in risk analysis depends on factors such as magnitude, duration, timing and whether the system recovers fully before the next event occurs. While previous studies have primarily examined the drivers and characteristics of individual extremes, less focus has been given to the concurrent or compounding nature of extremes across adjacent seasons. Thus, understanding the dynamics of such compound extremes, particularly dryness and wetness, is crucial. To address these concerns, a Multi Scalar Drought Index (MSDI) is formulated using precipitation and temperature data from three river basins (Brahmani, Baitarani and Cauvery) of eastern and southern India. The combinations of dryness and wetness, such as Dry‐Dry, Dry‐Wet, Wet‐Dry and Wet‐Wet, between consecutive seasons are analysed across four seasons (summer, rainy, autumn and winter). The prolonged dryness/wetness along with dry/wet year are evaluated from baseline (1979–2018) to projected COrdinated Regional Climate Downscaling Experiment (CORDEX) future period (2020–2099). The spatio‐temporal variations in intra‐annual dry‐wet extremes are identified using the Mann–Kendall test. The results suggest that the eastern Indian river basins, particularly the Brahmani and Baitarani basins, experience more frequent occurrences of compounding dryness‐wetness compared to Cauvery river which is a southern Indian basin. Future scenarios indicate a trend towards dryness during the monsoon season in Brahmani and Baitarani basins, with frequent wet extremes in late autumn and winter. Abrupt transitions between dryness and wetness are prevalent during the Rainy‐Autumn and Autumn‐Winter seasons in Brahmani and Baitarani basins. The increased frequency of compound dry‐wet extremes poses significant socio‐economic risks, including reduced agricultural productivity, water management challenges and heightened vulnerability of local livelihoods dependent on consistent water availability. The results of this study provide a scientific reference for sustainable agriculture and water resource management to predict future seasonal dry and wet alternations and develop effective mitigation strategies.