When arriving in India you have to collect your bags and clear customs in BOM. You can recheck your bags after clearing customs, but after that you have to go to the departures hall. Leaving the terminal is then no longer possible. If you want to leave the building you should not checkin your bags for the next flight.
View of the Intl-Domestic Transfer/Checkin desks after customs. Once you are done you have continue down this corridor which leads you to the domestic departure/checkin area.