I think it may not always be possible to combine magnifiers and diopters. Here's how I think it works:
A magnifying lens has a positive diopter. The corrective diopter would be positive only if you are farsighted. Adding these two would result in a stronger lens, and that ought to work. If you need a +1 diopter eyesight correction, and a +1 diopter magnification is added, then you have a +2 diopter lens, which seems reasonable.
But what if you are nearsighted, and need a -1 diopter correction. And let's say you want a +1 diopter magnification? Now we have (+1) + (-1) added algebraically, which equals zero. Window glass.
I have a feeling something is escaping me about this, but I don't know what it is. Maybe a magnifier is more than just a positive lens. Experts?