Yes, it is possible to both mechanical and chemical weathering taking place on the same materials. This is mainly happening in the regions where there's changing of seasons. You can have mechanical weathering when in the winter is very cold and the rocks get tighter and then the ice spreads the rocks with it's pressure, and then in the hot summer the rocks are spreading again, and in meantime the rain and the water and the chemicals in it influence in the chemical weathering of the rocks.
