sump pumps have a float switch which turns them on when the water level gets to a certain level. Using this principle, you can use the old pump to clean the new pump. Position the old pump so that its float switch activates at a higher water level than the strong pump, and so that the inlet for the old pump is right next to the filter for the strong pump. The strong pump will then pump the water out until the filter is too clogged, at which point the water will rise and switch on the old pump, which will suck the debris away from the strong pump, and the strong pump will take over again and pump the water out.
Of course, the whole premise is invalid since a properly set up sump system filters the water before it gets to the sump pit, so there wouldn't be any debris to clog the filter in the first place
