MS would have to change their law significantly. They have no training requirement - it's a cash and carry transaction - you have the money - you get the license.
Further, their background check system is useless in the meaning that it complies with NM Statutes. There's really no fingerprint requirement.
"Firearms Permit Unit -- >
§ 45-9-101. License to carry concealed pistol or revolver.
In the event a legible set of fingerprints, as determined by the Department of Public Safety and the Federal Bureau of Investigation, cannot be obtained after a minimum of three (3) attempts, the Department of Public Safety shall determine eligibility based upon a name check by the Mississippi Highway Safety Patrol and a Federal Bureau of Investigation name check conducted by the Mississippi Highway Safety Patrol at the request of the Department of Public Safety. "
Honors or reciprocity are only granted to states with requirements "Substantially similar" to NM Statue requirements.
All you can do here is carry openly - which is perfectly legal and done everyday.