One of Dorothy Sayers' mysteries dealt with exactly this, and the solution turned out to be old (but effective): the murderer had gradually built up a tolerance to arsenic, which is medicinal in extremely small quantities. He then poisoned his victim in public, by adding arsenic to *both* their meals (a omelet made at the table in a chafing dish). The victim died, the murderer was fine, and it took some very fancy work by Lord Peter and Miss Climpson to figure it all out....