Calandra added more, until the oil threatened to overspill her palm.
You can use overspill to refer to things or people which there is no room for in the usual place because it is full. With the best seats taken, it was ruled that the overspill could stand at the back of the court. people who move out of a big city because there are too many people living there, and go to live in new houses outside the city
{i} excess; act of spilling out; act of people moving out of the city due to lack of space (British)
Overspill is used to refer to people who live near a city because there is no room in the city itself. new towns built to absorb overspill from nearby cities