I have rooted caryopteris by two methods, layering and cuttings. The layering, I admit, has been done by the shrub itself. As I was pruning last fall, several of the lower hanging limbs had rooted, so I pulled them up and plopped them into pots with garden soil for growing on. Some cuttings I made earlier in the summer I simply put in a glass of water and they rooted as well. I've also done pieris japonica this way with good results.