Mumbai did not enforce the follow-on.
Mumbai have extended their lead to 299 runs.
Mumbai were 36 for the loss of one wicket at the end of second day's play.
Rest of India are trailing by 567 runs.
Jay Gokul Bista scored 104 off just 90 balls.
Suryakumar Yadav remains unbeaten on 88.
Mumbai won the Ranji Trophy title recently for the 41st time in history.
The domestic season-ending five-day Irani Cup game between newly crowned Ranji Trophy champions Mumbai and the Rest of India, commencing in Mumbai from Sunday, will provide fringe players a good opportunity to stake claims for the national team.
Jay Bista, who lost his place after a twin failure against Jharkhand in the Ranji quarter final at Mysuru, was made the 16th member of the squad following his double century for the victorious Mumbai under 23 team in the C K Nayudu final against Madhya Pradesh at Indore.