Poison is not cumulative. 

Rather, the counter will always be set to the more recent Poison Effect value being applied. For example: If you have a Poison 2 Effect Die on you, and a Baddie with Poison 1 targets you with that Skill, your Poison Effect Die should be set to 1. The same is true in reverse - Poison 1 can be bumped to Poison 2 if that’s what came second.