Such possibilities existed only before the Independence Movement gathered momentum and popularity under Indian National Congress. A division based on regional languages was never possible as the present linguistic states were not formed at that time. The large princely states like Hyderabad, Mysore, Travancore, Gwalior, Kashmir etc. also had a chance to go independent, if the British had left before the twentieth century. The regions directly ruled by the British would have solidified around existing power centers in a similar situation.Regarding the possibilities of a further divided India. I don't buy the Presidency theory of the three centres Bombay, Madras and Calcutta splitting from Delhi into three separate parts. At least not without some major flapping of butterfly wings. Congress after WWI was calling for the independence of all of India, not just minor parts.
But once the national movement under the Congress became strong, especially after the arrival of Mahatma Gandhi, the dream of a united India got entrenched in the minds of people. Then a division of the country would have faced the opposition of the people. That was why the partition caused such a large scale bloodshed.