Does increased rarity chance have a limit to how much can you increase it? Like lets say 100% maximum, or more. Or is it without a limit?
I found the accepted answer insufficiently complete so did some research and have continued to update this answer as I learn more.
Rare and Magic Equipment
The "Dragon's" prefix gives 24% IIR and the "of Excavation" suffix gives 26% IIR. It is possible to get both these affixes on the same item giving a total of +50% + implicit mods. These mods can spawn on Rings, Amulets, Belts, Helmets, Gloves and Boots with an Item Level equal or greater than 75.
Gold Amulets have an implicit IIR mod with max value of 20% and Gold Rings of 15%.
A level 20 Item Rarity support gem will add 57% IIR to monster drops killed with the supporting gem.
DoE = Dragon's [anything] of Excavation
Giving a total of +2,000% for chests in the vault*, +537% for kills with the support gem and +480% for everything else.
* Neither IIR from equipment nor gems applies to any chests, including large chests.
I've not started maps yet, they're level ~70+ end game content. Other than Vaults of Atziri other maps can also have +IIR mods.
Magical, Rare and Unique monsters have higher chance of giving up rare items. I was unable to find information about how much effect this has however it is combined multiplicatively with player IIR. There are also rare monsters with a very rare "Wealth" mod which further increases item rarity. I do know that the Item Level of drops from Magical and Rare can be +1 and +2 of the area level. (more powerful items are possible)
Being in parties increases the number of items that drop, not the rarity. However this will mean getting more rare items, in a round about way. You idealy want items with IIR and IIQ.
There is supposedly diminishing returns though I haven't seen any detailed information. This may just be pointing out that while +100% doubles what you get +200% is not another doubling. Or it may mean there's a logarithmic scale that tapers off how effective it is.
The max amount= of rarity you can get is only limited by the cap per item slot. Some unique items can get 100% rarity each and if I recall correctly there are even support gems which boost the rarity of the items found when you kill enemies with the skill.
The theoretical cap is probably +1922% from the Vaal unique map.