overflow into
To be so full that the contents of something spill into something else. The drainage ditch behind our house overflowed into our back yard after that huge rainstorm. The waiter wasn't paying attention when he was pouring my drink, and it started overflowing into my plate of food.
overflow into something
to spill over into something. The river overflowed into the surrounding farmland. The water in the bowl overflowed into the sink.