There are threads on this already, and many possbilities exist for how to do this, particularly in regard to India. However, most of them are difficult to achieve given the partition implemented in our timeline that was meant to largely be religious in nature. But, here's a go with a similar initial partion to get us started.
August 15, 1947: India is partioned into India, Pakistan, and Dravidastan. Due to location, Hyderabad and Kashmir hold on to independence-for the moment.
1950-1965: Border skirmishes occur between India and Pakistan. Due to butterflies, Goa, Daman, and Diu are not annexed and later form the Republic of Goa.
1969: South Asian War; Indo-Pakistani border war breaks out as a Bengali nationalist movement takes power in East Pakistan. The war lasts until 1972 with both sides battered and broken, and the map is remade. West Bengal joins East Pakistan to form Bangladesh, and the easternmost extension of India forms the Republic of Assam. Otherwise, borders revert to where they were before the war.
Successors to British India, 2011 CE:
- India
- Pakistan
- Bangladesh
- Assam
- Dravidastan
- Hyderabad
- Kashmir
- Goa