Is it possible to have two types of psoriasis present on your body at once?

Yes: However that really matters little as treatment options remain basically the same.

Different appearnces: There are 3 major clinical types of psoriasis - namely plaque, erythrodermic, and pustular. It is unlikely to have combinations of these in any one individual but one can evolve into the other. It is important to differentiate among these three types since the treatment can be different depending on which type it is. Most people have plaque psoriasis but it can have many different appearances.