If radio station call letters must begin with either $\mathrm{K}$ or $\mathrm{W}$ and must include either two or three additional letters, how many different possibilities are there?

Step 1 ：Break down the problem into two parts: possibilities with two additional letters and possibilities with three additional letters.

Step 2 ：For the two additional letters, there are 2 choices for the first letter (K or W) and 26 choices for each of the next two letters (any letter from A to Z). So, the total number of possibilities is \(2 * 26 * 26\).

Step 3 ：For the three additional letters, there are again 2 choices for the first letter and 26 choices for each of the next three letters. So, the total number of possibilities is \(2 * 26 * 26 * 26\).

Step 4 ：The total number of possibilities is the sum of these two, which is \(1352 + 35152 = 36504\).

Step 5 ：Final Answer: The total number of different possibilities for the radio station call letters is \(\boxed{36504}\).