Depending on what codec (and therefore the kind of tags you use), you can add multiple covers and give them descriptions in mp3tag. If you meant that you want "Album Art 1" and "Album Art 2" to be literal names, the description is where you'd put that. If you meant that you want them to display in a certain order within mp3tag, I believe the one designated as "Front Cover" will display first. If you have multiple "Front Cover" entries, they're displayed inverse of the order they were added. (I.e., you'd add Album Art 3 first, then Album Art 2, and finally Album Art 1 to get them ordered as 1,2,3.)
Ultimately, what matters more is making sure your players handle the artwork the way you want. How mp3tag displays it isn't as important.
I use ALAC, which has a few annoying tagging limitations. You can only have "Front Cover" and "Back Cover," so in the situations you're talking about, I usually just add the Box cover as "Back Cover."