One common question that I get is whether it is OK to mix two tires of one type with two tires of another. Certain mixes are expressly forbidden, such as mixing two snow tires with two summer or all-season tires. But even two different pairs of tires of the same general type can lead to unpredictable handling.
Even if the new pair of tires has better ratings than the two tires remaining on the car, the performance is usually worse than a matching set of either type. Some people mix tires and never notice any adverse effects, but many times the result is some spooky, unbalanced behavior.
Sometimes the tire on the car may no longer be available, and your budget might not allow a purchase of four tires right away. At that point, the best we can do is try to match brand, speed rating, tire type, and tread pattern as closely as possible, and hope for the best.
I would never mix tires on a car unless there was no other choice whatsoever.