There are a great many disorders that are often comorbid with Asperger's. The only ones that categorically cannot be diagnosed in addition to Asperger's are the other autism spectrum disorders--you can have only one of those, as such a diagnosis rules out all the others. There is also a note that ADHD and autism can't be diagnosed together because autism diagnosis takes precedence over ADHD diagnosis; but many people believe that this doesn't make any sense because even though many autistic people do have ADHD symptoms, there is a large subgroup that does not.
So, yes. You can have multiple diagnoses. This is more often than not the case.
Paranoia is not a diagnosis in and of itself; it's a symptom of other problems, from justifiably being afraid that people are going to hurt you simply because they really do intend to hurt you, to two of the personality disorders (avoidant and paranoid), to practically any psychosis (bipolar, schizophrenia and its cousins, and depression with psychotic features). Plus, what you might have mightn't be paranoia but be better described as anxiety, which can of course be put down to anything from a natural response to circumstances (people are not actually supposed to be anxiety-free all the time), to any number of physical and mental problems.
Um. So yes. If you're Asperger's, and you're having significant problems from something you can't put down to AS, you should talk to your doctor about the possibility of something other than AS going on (response to your circumstances, physical illness, mental illness, skills you need to learn, etc.). These things do way better when they're dealt with before they get really troublesome.