Naturally this is just a single experiment, but it does offer some statistically significant results for combinations of antibiotics and lavender, peppermint, and cinnamon oils:
The lowest oil concentration they see synergy is 0.078% v/v. Assuming that's roughly the same as w/w%, that's 53 grams of oil that would have to be distributed throughout the body of a 68 kg person.
http://www.ncbi.nlm.nih.gov/pubmed/23537749