If you are not on a strict water-only fast then anything other than water will definitely interfere with the fasting process of cleansing and healing.
However, if you are on a juice/water fast (which means you are feeding) then additional vitamins will not do any harm as long as they are of a high quality.
Both juice and Water Fasting do have their benefits but in my own opinion (and that of many Fasting authorities in the past) Water Fasting is superior in terms of both cleansing and healing.