forsure
I can see no reason why vitamins would not be allowed. The OP website suggests a diet of whole fruits and veggies and lots of water. I've been on it for 6 days and have been eating fruit - dried and fresh, salads, tehini, and a little bit of chicken, and some nuts and seeds. The OP seems to liquefy anything in its path, so I don't think you need to be too worried about your diet as long as it's not all candy and ice cream - LOL
Good luck, and can you keep up posted on how it goes?