Besides the 12 miniatures that come in the base box, what would be the recommended additional player positions to get a team up to 16 players from 12 for a human team?
If you're asking what you should buy minis wise, I recommend maxing out all positionals (Throwers, Catchers, Blitzers), with the Ogre being optional depending on whether you want a Big Guy or not in the team.
If you're talking about in-game team design, I say don't go to 16. You want to keep your roster lean to keep your Team Value down.
You'll want 4 Blitzers eventually, 2 Throwers (one for offense and one for defense) and a certain numbers of Catchers/Ogre based on whether you're focusing your team on running or passing plays, and to have somewhere around 12-13 players at most.
That is, unless campaign mode changed a lot since LRB6.0