Thank you for your question and welcome to Just Answer.
Yes, if you have caps on your teeth you can still have orthodontic treatment. Moving teeth with orthodontics involves bonding small brackets on to the front surface of all the teeth. Then a single thin wire is placed into the groove of all the brackets and tied to place with small rubber elastics. Unfortunately, these brackets do not bond onto the surface of porcelain. To get around this difficulty, any teeth with porcelain caps have a small, thin metal band placed around them that has the bracket attached to the band.
I hope this answers your question. If you would like to discuss this further or have any additional questions, please reply to my answer and I will get right back to you.
Sincerely, XXXXX XXXXX DDS