Budwig actually recommended not taking other supplements while on the Budwig protocol. So throwing everything everything else and the kitchen sink while on Budwig could be counterproductive.
However, I do actually do a fair amount of supplementation given that the world is more toxic and certain nutrients (like iodiine) are less present in the food supply than they were in Budwigs hayday. I do supplement with iodine, superfoods, Vitamin D (Budwig recommened 2 hours per day in the sun), juicing, oil pulling, hot saunas, selinium, B-12 etc. I don't know whether Oleander would work at cross purposes with Budwig or not.