Question
If we have already married with a standard civil ceremony, can we have a Jewish ceremony as well?
Yes, absolutely. Provided you are both Jewish and free to marry each other according to Halacha, you may (and should!) also have a Jewish wedding ceremony. Just make sure to tell the officiating Rabbi that you are already had a civil marriage ceremony, so that he will know that he does not have to do the paperwork.
Answer
Having a Jewish marriage ceremony is a Mitzvah, and doing so will strengthen and enhance your married life.
Mazel Tov!
Rabbi David Sedley