First off, almost everything stacks in this game - the question is more about how. As you seem a bit unfamiliar with how stacking works in general, I will explain a bit further before I give my best guess.
How you would calculate the stacking in either case
With two bonuses, one of 15% and one of 20%
Simple, and as you said. The buffs percentages add up, and your damage is multiplied as
[Total Damage] = [Damage] * (1 + 0.15 + 0.20) = [Damage] * 1.35.
When damage increases stack multiplicatively, they are applied one after another as follows:
[Total Damage] = [Damage] * (1 + 0.15) * (1 + 0.20) = [Damage] * 1.38.
As you can see, this is a greater damage increase than the additive one. In general, increasing modifiers get more powerful through multiplicative stacking, and reducing modifiers get weaker (such as how damage reduction works).
What stacks in what ways?
I wasn't able to find a specific source, but generally (I say this with a bit of hesitation, as there are many exceptions) one can sort the buffs and/or debuffs into groups. In general (again, with exceptions), buffs and effects within the same group stack additively, and different groups stack multiplicatively. This is to preserve balance. Examples of groups include:
- +% Elemental Damage (player)
- +% Damage (player)
- +% Damage taken (monster)
As I said, effects within the groups stack additively (two +% Fire Damage buffs of 20% add up to 40%, not 44%), and groups stack multiplicatively (+40% Fire Damage and +30% Damage gives you a total bonus of 82% instead of 70%).
The main common exception to this is that almost all reducing percentage modifiers stack multiplicatively with themselves (% Damage Reduction, % Cooldown Reduction, % Resource Cost Reduction etc.).
Your specific case
Following the logic above, both of these things fall within the same group (+% Damage Taken), and would be applied additively (adding up to a 35% increase). However, this just seems the most likely case, so don't take it for truth (please correct me if I'm wrong and I'll update).
In either case, the difference between 1.35 and 1.38 is difficult to measure given the large variations of damage numbers that naturally occur (and the difference is much smaller than the one you put forth in your question).