When New Mexico first began issuing permits you needed to qualify with every combination of action type AND caliber that you wanted to carry. If you qualified with a .357 magnum you could not carry a .38 Special unless you also qualified with it.
Recently we had a change to the law where qualifying with a particular caliber of an action type allows you to carry anything up to and including that caliber. So, instead of qualifying with a half a dozen weapons in order to cover all the bases you only need to qualify with two, a semi-auto and a revolver. I used a 1911 in .45 ACP and a Ruger Vaquero in.45 Colt (I now have a S&W 22-4 in .45 ACP, so I will use it next time.). This allows me to carry anything I want, including .44 magnum since the law is based on caliber, and not power level.
One of the really stupid things to also be added to our law was the prohibition on carrying more than one concealed weapon, so no BUGs. We need to get that changed as well as the prohibition on carrying where alcohol is sold. You can't legally carry in most Wal-Marts, grocery stores, or restaurants. We either need to get some type of 51% rule, like Texas, or a ruling that it doesn't matter where you carry just so long as you maintain a low blood alcohol level.