No, they specifically do not stack
From the basic rules:
Occasionally, your proficiency bonus might be multiplied or divided (doubled or halved, for example) before you apply it. For example, the rogue’s Expertise feature doubles the proficiency bonus for certain ability checks. If a circumstance suggests that your proficiency bonus applies more than once to the same roll, you still add it only once and multiply or divide it only once.
Emphasis mine. Even if you somehow took proficiency in the same skill twice (I believe the wording in the official PHB always says choose more or additional skills), it wouldn't apply because you can't benefit from a proficiency bonus more than once.