Do features that allow you to add twice your proficiency bonus, under some other name, stack with Expertise?
For instance, dwarves' racial Stonecunning trait, with bards' Expertise as applied to History checks, to identify the origin of stonework.
The text of Stonecunning is reproduced below:
Whenever you make an Intelligence (History) check related to the origin of stonework, you are considered proficient in the History skill and add double your proficiency bonus to the check, instead of your normal proficiency bonus.
And, for good measure, the relevant portion of Expertise:
Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.
Best Answer
Your proficiency bonus can only be added or multiplied once by any ability or combination of abilities
From the Basic Rules / PHB p. 173:
Thus, any features that would result in you multiplying or adding your proficiency bonus more than once would not stack - you only get to add or multiply or add your proficiency bonus the one time.
Example: Stonecunning and Expertise don't stack
In the case of your example, here is what they would both do to a roll:
Note how both features do exactly the same thing: allow you to add double your proficiency bonus to a qualifying check.
Here is what it would look like if you let both apply to the same roll:
or
However you do the math, allowing both to apply to the same roll would result in either multiplying your proficiency bonus more than once or adding it more than once. Either way, it violates the rule and is thus not allowed.
Example: Mastery Ioun Stone and Expertise would stack
A rare few effects add a static bonus to your proficiency bonus. These additive effects are highly uncommon though. Most features multiply your proficiency bonus and thus fall into the previous example and do not qualify. An example of an additive effect is as follows:
The Mastery Ioun Stone says:
Since this only adds one to your proficiency bonus, there is nothing preventing it from stacking with Expertise.
You still only add your proficiency modifier once to the roll and you only multiply it once and thus they stack validly.