Currently, if you have a concealed carry permit from your state, it's only good in so many other states. There are multiple problems with this.
There's the legal side: a state issuing a license should have that license recognized in all other states and DC (just like I'd want to see INRE any marriage licenses).
There's the criminal side: people make mistakes and carry into a state that doesn't recognize their permit. The best example I can think of is Wisconsin. Their original standards for concealed carry led other states (quite a few actually) to recognize their permit. They changed their standards and now only 25 states recognize their permit. Obviously this doesn't excuse ignorance or not double checking local law if you leave your state, but this situation could be easily fixed with a national carry system.
My suggestions: a three tiered system (with the third tier having 'mini tiers').
Right to Keep and Bear Arms is a DKos group of second amendment supporters who have progressive and liberal values. We don't think that being a liberal means one has to be anti-gun. Some of us are extreme in our second amendment views (no licensing, no restrictions on small arms) and some of us are more moderate (licensing, restrictions on small arms.) Moderate or extreme or somewhere in between, we hold one common belief: more gun control equals lost elections. We don't want a repeat of 1994. We are an inclusive group: if you see the Second Amendment as safeguarding our right to keep and bear arms individually, then come join us in our conversation. If you are against the right to keep and bear arms, come join our conversation. We look forward to seeing you, as long as you engage in a civil discussion.
First, let's look at Vermont. Bluest state in the union and allows anyone to carry a firearm concealed if they're legally able to own a firearm. No permit required. The problem here is that since there's no permit, who recognizes Vermont? The first tier of the national carry system would be state based. You never leave Vermont? You don't ever need to do anything other than stay a law abiding citizen. Arizona is similar. They have Constitutional Carry (no permit required) but they also have another option which will bring us to tier two.
Tier two is basically what we have today. Continuing with the Arizona example: say you want to leave Arizona and carry concealed. You can take the approved concealed carry course, get your permit, and where you're able to legally carry is based on whatever state agreements have been set up at the state level. Arizona permits are recognized by thirty two other states right now. But what if you go to California for some reason and you'd still like to carry?
This brings us to tier three. This is the suggested new tier for national concealed carry, administered at the federal level and good in all 50 states, DC, Puerto Rico, and any other US territory. I would suggest multiple levels of this license, similar to how we have multiple levels of a driver license (chauffeur, CDL, regular, etc). I'd also like to point out that none of these are just "take the class and you pass" classes.
The basic level of tier three would be taking a course that is federally approved, with range time, legal time, class time, and a federal background check. One of the more important parts: this would be shall issue. (I'll define shall/may issue at the bottom.) This basic level would ensure that you're able to carry in all 50 states and DC, regardless of local law.
The plus level would take all of the training of basic and add on additional training of the law enforcement variety. This would include advanced deescalation techniques, additional marksmanship training, and more legal time. You'd be able to carry in areas that would normally be off limits like hospitals, casinos, and the like. This would not override private property owners wishes (for example: if they posted a No Guns sign when the sign has the force of law).
The next level (what's better than plus? double plus!) would include all the plus level training and include Federal Flight Deck Officer (FFDO) training. FFDO training is law enforcement training that currently (once passed) arms volunteer pilots on commercial flights to prevent highjacking. This would be open to the general public, not just pilots.
There's probably room for more levels but I'm going to leave it here for now. This should make for an interesting conversation in the comments.
Shall issue: a shall issue style of concealed carry is when you meet all the requirements (EG: not a felon, took the class, passed the background check) then the issuing authority doesn't have discretion to issue a license or not. They just issue the license. Think Michigan or Arizona or Washington or Illinois.
May issue: a may issue style of concealed carry is when you meet all the requirements but the issuing authority can still tell you to go whistle and deny your permit. Think New York or Cali or Delaware or New Jersey or Hawaii (which basically denies ALL permits).