You should be able to give a potion of see invisible to a shopkeeper while you are invisible. They will then quaff it, and stop blocking their shop door. Depending on implementation, if the shopkeeper’s see invisible is temporary and later times out, once they can no longer see you, they will again block the door.

If an invisible monster (or the player) is doused in a potion of see invisible from a thrown bottle breaking on them, they become visible again (unless extrinsically invisible which overrides this).

Quaffing cursed invisibility removes the invisibility intrinsic if you had it. Possibly the same for see invisible.

The cursed potion of see invisible removes any see invisible intrinsic that the player has.