This will only confuse the cat and most likely make the situation worse. If you add a new cat to your family, you should also add another litter box. The general rule of thumb is to provide one litter box per household, and one litter box per cat. Try a different style of litter box, one covered and one uncovered. Always keep the litter box clean.
Many cats are very particular about cleanliness.
That means scoop the box daily and completely clean every week. If you change brands, however, gradually replace the old litter with the new one over a five day period. And beware of litter material that contains heavy deodorizers or perfumes. Keep the litter boxes in quiet, convenient locations, away from the household bustle of adults, kids, dogs, etc. And remember that cats do not like to eliminate in the same area where they eat and drink.