The House passed a bill last December that greatly expands background checks and that mandates concealed-carry reciprocity among the several States.
The Senate should take up that bill without further delay and pass it as well. With the much broader background checks, there’s no longer any rational argument for opposing concealed-carry reciprocity.
It’s a pipedream, though; there aren’t enough Progressive-Democrat Senators willing to vote for cloture. The lack of progress is too important to them as a campaign issue.