Just doing a quick and dirty check, there is absolutely no upgrade path for WXYK that I can see.
The next class up from A would be C3, which would only increase the primary service contour by about five miles. To meet minimum separation from the 107.1 in Hattiesburg AND the 107.1 in Hammond, Louisiana (both are also class A's) the site would have to move east to Ocean Springs, south of US-98. But that would short space it to the Pensacola station on 107.3. In fact, if I'm not reading things wrong, WXYK is ALREADY short-spaced to WRGV so it couldn't move further east anyway.
Theoretically speaking upgrading to a C3 would increase their coverage of Pascagoula and Gulfport at the expense of Bay St. Louis, but it would probably necessitate a change of city of license to Ocean Springs or something because Gulfport would probably no longer be under the 70 dBu city contour. Also, over half the radiated power would be over the Gulf of Mexico.
I'm not engineer, however, so there may be a way around it. But it would a big headache for very little benefit, imho.