It's not that you have extra saliva it's that you are not swallowing enough. Your natural swallowing reflex is controlled by muscles that get the or don't get the signal from the brain which is caused by parkinson. That's my opinion anyway

Usually swallowing more often helps. With PD your tongue doesn't work and your swallow reflex slows down. The saliva collects under your tongue. Think about what your pillow looks like some mornings

@KatyK: My medications make my mouth very dry so I always carry water with me. However I have times when I do drool. My speech therapist noted my drooling and helped me be more attentive to the position of my head. If I notice I am drooling, I need to lift my head straight or even a little bit back so the saliva drains down the throat. With PD your mouth does not measure the saliva plus there is difficulty with normal swallowing.

Don't know of cure it seems to come with PD
I reccomend you talk with your primary care provider

My spouse has tried Botox injection in salivary gland and Atropine drops (now off the market) and they caused other problems. So he continues to be uncomfortable with lots of saliva.