Under the sea, some rocks do grow, albeit very slowly.
Credit: James Brune
Rocks don't eat, drink, or take their vitamins, but they do grow.
Observing the process, though, is less interesting than watching paint dry. Rocks called iron-manganese crusts grow on mountains under the sea. The crusts precipitate material slowly from seawater, growing about 1 millimeter every million years.
Your fingernails grow about the same amount every two weeks.