I'd say sure you can plant some different alliums in the same bed, but best not to plant alliums in that same bed next year - rotate them somewhere else. At least, that's recommended to reduce risk of losses by pest or disease. Some people seem to do alright using the same bed for several years so for sure it depends on where you are and what the resident pests/diseases have to say.
The Egyptian Onion is perennial, so although you can move them if's more to the point to put them somewhere you want to leave them for a few years. I got some great topsets from a friend last fall and stuck them into a couple of small beds or as borders with other perennials - I must say they are very ornamental with their tops happening. I'd like to try the little topset onions for pickles when they are ready.
