One thing you see in movies and books sometimes is a person will take small doses of poison over a long period of time and thereby gain immunity to the harmful effects of that particular poison.
Is there any poison for which this could be true?
Iocane.
I seriously doubt it. Napoleon apparently died from slow poisoning.
There are very few poisons that one can’t develop some degree of tolerance to.
You astonish me, Sir.
It’s called Mithridatism, named after Mithridates VI, the King of Pontus, who supposedly consumed small amounts of poisons over his lifetime to build up a resistance to them. According to legend, he attempted to commit suicide when he was about to be captured by his enemies (better than being slowly tortured to death) but wouldn’t die because he had built up such a tolerance to poison over his lifetime. He ended up falling on his sword to finish the deed.
The principle does work with a lot of poisons, but I would call it a “resistance” rather than an “immunity”. You never become fully immune to the poison. You just end up with a higher tolerance than normal, and can often survive doses that would kill most people.
There are some modern documented cases where someone has been poisoned using small amounts of some deadly substance over time, to make the person appear to get ill and die from natural causes. In some cases, the victim is found to have survived levels of the toxin that would be lethal to most people for extended periods of time before finally passing away.
Mithridatism is basically how they treat peanut and other allergies.
Snake handlers will also use Mithridatism to build up a resistance to the venom from the snakes that they handle.
Mithridatism doesn’t work for things like heavy metal poisoning. You also can’t build up a tolerance for cyanide.
I shall bear that in mind, thank you. 
It certainly does work for heavy metals.
The problem with heavy metals, and a great many other poisons, is that inducing tolerance to acute poisoning in this way results in chronic poisoning. Nonetheless tolerance can be developed.
That does seem to be conflicting evidence.
This looks like the plot for a murder mystery where the murderer builds up a resistance to a poison and then takes an equal dose to the one he wishes to kill making it look like an accidental poisoning.
Because everything can kill you in large doses, for example even just an excess dose of water can kill you.
There are two ways to develop the tolerance
- teach your body to make antibodies
- teach your body not to have reactions such as anaphalaxis, high temperature and so on.
There are also hundreds of others, including downregulating affected proteins, increasing enzymatic breakdown, diuresis and so forth.
Unless the poison’s ethanol, then they just call you a drunk. T’ain’t fair, doc.
I recalled, as a child, reading about arsenic eaters in Europe who could consume lethal doses with no ill effects due to the tolerance they had built up. A quick look lead me to this interesting piece: THE ARSENIC EATERS OF STYRIA
I’ve heard that it works well with iocaine powder.
It’s been done.
Strong Poison by Dorothy L. Sayers