Here's how I got 16 vivs on standard map. Give it a try it's a blast, then maybe you can help me figure out the luxury problem
Open your CivIII folder
Run "Civ3Mod"
Click "Edit" in top middle of the toolbar
Click on tab "World Sizes"
Select "Standard" (you can do this with any of the map sizes)
Change the "Number of Civilazations" from 8 to 16
Optional: Change distance between cities from 12 to 8 (same starting distance as on tiny maps, still seeing if this makes a difference)
Exit and save changes
Next game you start you will see all 15 other slots available for the other civs; play with all 16 or block some out for however many you want to play with. Not sure about how luxuries will appear if you don't choose 16, but if you do choose 16 I've only been able to get 6 of the 8 luxuries to show up.
Have fun with all the new neighbors
let me know how it goes