LA Resident permits are among the most recognized in the country. Some other States' permits are recognized by 33 States, ours is recognized by 32. I do not know of any State that is recognized my more than 33.
Since there are several States that do not recognize permits unless you are a resident of the State whose permit you have, there is no way to have your permit be recognized in more places with one permit than by having a LA CHP (if you are a LA resident). UT is the closest second.
LA= 18 States you can't carry in (plus DC)
FL non resident= 23 States you can't carry in (plus DC)
UT non resident= 20 States you can't carry in (plus DC)
These numbers are to the best of my understanding, I plan on double-checking them again later.