Q:

Is Poison Resistance Over Time with Anti-Toxin Possible?

I've got in-world poisons, often with real-world analogues (like belladonna) but in building the social structure of the back-stabbing nobility, I began looking at poison resistances and antidotes. 
Basically, those who protect royalty also try and find a way to up their poison resistance, and during especially troubled times, put anti-toxins in their foods.
I already know about Mithridatism, "the practice of protecting oneself against a poison by gradually self-administering non-lethal amounts." But this is not what I am wanting to do.
I am looking to gradually dose the king with a general anti-toxin that's proof against most poisons. My question here is, are there real-life analogues that would be that broad? And if not, what combinations of things would be best? 
EDIT: Don't worry about tech level--can be anything through to today's science--this is set in a Renaissance-type world, but I can adjust anything to fit because the world is pretty flexible and not entirely Renaissance, I just need some jumping off points to create what's needed. 
THE PROBLEM: 
Right now, I am finding that many things which wipe out poison aren't actually good to ingest on the regular (like charcoal)--and I am looking for things that will. Stuff that's close is ok, because I can use it as a starting point at least in building that bit of my world.

A:

This seems possibly unlikely. One problem in answering your answer is an uncertainty in the technological level of your world. Traditional poisons are deadly herbs and mineral-derived chemicals. Unless your world possesses herbs or other planet materials that can act as counter-agents to a given class of toxic herbs, then this may be improbable. 
However, this argument can be turned on its head. Since, it's your world, you are free to introduced varieties of poisonous plants that have other plants which naturally produce substances that either denature the poisons themselves or bind to the receptors in the intended victim's body to prevent the toxins from binding and causing the death of the person.
By and large, what you are contemplating to an anitoxin (or class of antitoxins) that work on equivalent lines to to a snake antivenom. While this requires post-medieval medical science and technology to facilitate and make practical (in the real world). There is no reason why in a constructed world, as argued above, there could be classes of substances (preferably botanical or even animal derived) where some are poisons and others are their equivalent antitoxins.
Plants have a long, protracted and extensive evolutionary history of developing defensive substances to ward insects, fungi, bacteria and herbivores. Effectively, these are poisons. Therefore, it is possible that the various predators on poisonous plants will develop on their counter-agents. This can include developing antitoxins or metabolic pathways to detoxify any poisons.
If you allow yourself the luxury of going one step further, some but not necessarily all** antitoxins may have a vaccine-like action on persons to whom they administered. This will have desired effect to facilitate a situation along the lines you are hoping for in your world.
**: You don't want every poison vaccinated against, this will dissipate dramatic tension. Also, some vaccines can wear off. So keeping up your doses of antitoxin may still be necessary. Again this is good for dramatic tension. We all know you don't want to make things too easy.

A:

Cytochrome_P450s as a class are the enzymes which the body uses to break down most organic molecules - including drugs, toxins, ethanol and presumably organic poisons.
https://en.wikipedia.org/wiki/Cytochrome_P450#Drug_metabolism
In the presence of lots of substrate the liver upregulates the given cytochrome p450 molecules needs.  Chronic alcohol, for example, upregulates CYP2E1.  Other cytochromes which handle other toxins can be upregulated by specific substrates (and inhibited by others).  This is why you are not supposed to drink grapefruit juice with certain drugs - the juice inhibits the CYP and thus the metabolism of the drug. 
So to get the CYPs good and induced you could drink inducers.  I think fortified wine (of the Night Train variety) laced with plentiful capsaicin would be a fine start.
For heavy metal detox the body uses glutathione.  It is not so straightforward to induce.  It is interesting, however, that the mechanism of glutathione is its abundance of -SH sulfhydryl groups which bind lead, mercury and the like.  Hair is also very rich in free sulfhydryl groups and hair is the main ingredient in the well known antipoison, bezoar. 

Bezoars are basically hairballs.  This one ought to last you a couple of days. 
So: to cover against arsenic, mercury and the like I recommend finely chopped bezoars (of the hairball variety!) to be added to the capsicum wine.  Shake well.  Serve cold.  
One might object that no less an august personage that Ambroise Pare demonstrated bezoar to be ineffective by testing it on a cook condemned to die: instead of hanging the cook opted to eat a bezoar then poison, and died in agony.  The poison chosen was lye.  I do not think there is anything which will induce an immunity to lye.  

