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Let's say I'm a multiclass rogue/ranger and I have taken Expertise in survival checks. Now, if a ranger is in their favored terrain it says they double their proficiency bonus in intelligence and wisdom checks relating to you environment. If I am in my favored terrain and use my already doubled survival check, will it double again?

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No. Per Basic Rules p7 and PHB p12:

Occasionally, your proficiency bonus might be modified (doubled or halved, for example) before you apply it. If a circumstance suggests that your proficiency bonus applies more than once to the same roll or that it should be multiplied more than once, you nevertheless add it only once, multiply it only once, and halve it only once.

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