During the Border-Gavaskar trophy 2004/05 in India, Rahul Dravid scored 619 runs in 8 innings which included one century and 3 half-centuries.
When India toured the West Indies in 1970/71, Dilip Serdesai scored 642 runs which included 3 centuries.
Yashasvi Jaiswal has already broken many records during the ongoing India vs England Test series. Jaiswal has scored 655 runs with 1 game to go.
Virat Kohli was heavily criticized as he failed during India's tour to England in 2014 but during his next tour to England, he smashed 655 runs.
During India's tour to Australia in 2014/15, former Indian Test skipper Virat Kohli amassed 692 runs in 8 innings which included 4 centuries.
Sunil Gavaskar scored 732 runs during the West Indies' tour of India in 1978/79. Gavaskar played 9 innings to score these many runs.
During India's tour to West Indies in 1970/71, Sunil Gavaskar had an outstanding batting average of 154.8 as he scored 774 runs in 4 Test matches.