I tried to add a level 70 nephini to my party, but it says I can only command pets up to level 40? Does this mean once my pets reach level 40, I can't use them anymore?

Your current user level (displayed under your name and above your avatar on the forums) is 40. This means that you currently cannot use any pets above level 40 in your party (though you can use them for missions, breeding, etc.).

Once you personally level a pet from 40 to 41 (be that through battling, missions, exp orbs, whatever), your user level will increase to 41 and you can use pets up to level 41.

And so on up 'till you reach the current level cap, which is 70.

Oh okay. Thanks for the help!