If your car comes with radials and has the various forms of traction control, ABS, handling packages. etc. you will see that the service manual says you should replace all the tires at the same time. If you have a damaged tire that cannot be repaired many tire dealers will refuse to change just one tire. They are following the manufacturer recommendation.
I recently saw a neat workaround for this. The next time you need tires get a 5th one for the spare. When you have rotate the tires make sure the spare is rotated as well. That will increase the life of the tires by 20% since it is an additional tire.
But there is another advantage. If you do have one tire that is damaged and cannot be repaired, you replace it with the spare and then drive normally until the next tire rotation. Then rotate only 4. You will not have to replace more tires than you need.