Here in Florida, Callisia fragrans can take over ...fortunately they are easy to pull up. I cleared out a couple of beds covered in both the solid and the variegated variety last year. Mine began from a small pup I received in a trade back @ 2008. The plant is listed in Florida as a Category II Exotic Pest Plant which means it's a species that shows a potential to disrupt native plant communities. It may at some point end up becoming a Category I invasive. I still have a few growing behind the deck and in a bed at the corner of our driveway.
Cinta, has yours bloomed yet? The flowers are small but so very fragrant!
One of the flower beds I cleared of the variegated variety and the solid one with red foliage from sun:
