I personally, I would be very weary of giving him any more. Just as in humans, a vaccine reaction is a contraindication to further vaccines (you can read that on the CDC web site)
I did research on vaccines, and I know that this is contravercial and many people will get their feathers up, but after I researched, I chose not to vaccinate my two. (they were vaccinated by their breeders, but I used detox remedies to help them with the toxins) I go to a holistic vet, and a homeopath, and I protect my two homeopathically and by making sure that their immune systems are as strong as they can be.
My advice is do some research. If you do chose to vaccinate, you can ask to only get one at a time and wait a couple of weeks before getting another. This will enable their little immune systems to deal with the toxins in the vaccines more effectively, rather than getting them all at once and overloading the immune system.