There are printers with white ink. Roland has some, Mimaki, there are some retrofited epsons small flatbeds with white, and some UV flatbeds with white. Also there is an Epson printing with white:
"Capable of printing directly on both ink jet coated clear and metallic films, in roll or cut sheet, up to 24 inches wide, the Epson Stylus Pro WT7900 can proof virtually any size print job thrown at it. Whether you're creating contract proofs of various packaging products requiring a clear or metallic base, or producing color accurate packaging mock-ups or prototypes, the Epson Stylus Pro WT7900 can easily proof your most difficult flexographic and gravure print jobs."
So, there are some solutions, BUT I advice you not to buy one, unless you are going to print alot with white.
Why?
1. Usualy, white is not opaque enough and you may end printing white in multiple layers.
2. Daily maintenance. You have to shake the white carts every day. You have to clean the head every day. You have to print (alot) of white every day. Because white pigments are very heavy and they settle down in the carts. The reality is the pigments ends on the bottom of the carts anyways, even if you shake them in a couple months. Some printers have some sofiticated mechanisms to recirculate white ink to prevent deposits. But this is only for the head and tubes, not for the carts.
I have a retrofited Epson 4880 flatbed with white inks and i end replacing white ink with cleaning solution in the carts.
If you have the opportunity, find someone else with a white ink printer and outsource the job. Or outsource the white part of the job to a silkscreen printer and do the color job yourself on tpo of it.
Edit: i almost forgot: it is extremly slow process to print with white
