Technically, you can use almost any cactus to graft another one onto. The diameter of the core has to be similar, but you can graft a Mammillaria onto a Suguaro. There used to be a Russian guy, Peter Lapshin who had a site and covered grafting with pics of his creations. A search for him might enlighten you, just reading his site is interesting. As I recall, he mostly used Pereskiopsis, but sometimes other genera.

I'm not sure why you have trouble with Pereskiopsis. They like a wide pot, lots of water when they have leaves, and dry when they lose the leaves. They do get big fast, and I'm not sure how you grow them in a house. If there is a botanical garden around, maybe you could donate one, then volunteer to prune it for them. I did that with P. grandifolia. They grow fast into a shrub and need frequent pruning to keep them under control. What species are you using? I haven't grafted for a long time, used grandifolia.

Hi,
I'm using spathulata. When I had them outside in the fall they were doing great. I have them under fluorescent lights and a room temperature around 60 F. They are suppose to tolerate temps down to 55 F. I have epi's without lights and the same temperature and they are doing great. The fall temperature's around here are on the cool side but the Pereskiopsis had no trouble with that. Do they lose all there leaves at once or just a couple at a time ? How long can they survive without any leaves? I have one that is bare except for the glochids.