What if you grafted a wild olive branch onto a cultivated olive tree?

Grafting is done for several purposes, but most commonly in the olive oil industry it is to get the hardy roots of one variety with the fecundity of another variety. The whole point of grafting is that each part of the grafted tree keeps its original character. The variety used for the root stock may be resistant to fungus or other pests but has a small or low yield olive. The graft may have weak roots but large fruit with high oil content. The resulting tree has the best of both varieties

Fruit trees are commonly grafted for backyard use so that one tree yields several types of related fruits. A peach tree could be grafted with two different types of peaches and a nectarine. You would probably not see a grafted tree with unrelated species such as peaches, walnuts and avocados on it.