The following page of the Disgaea RPG guide answers what to do with copies of the characters. You will also find out what the N.E. Prinnies are for.
If a character you already have joins your party, you can use it as a copy to strengthen the original.
Go to Facilities (the icon at the bottom of the screen), and then go to Mao's Lab. Click on N.E. (Nether Enhance) and select the character you want to strengthen.
Click on the copy of the character from your hero list and then on the Nether Enhance icon. You need to pay HL coins to strengthen a character.
The number of enhancements and effects obtained is under the character's name.
Instead of using copies, you can also strengthen characters by using a N.E. Prinny. These items are extremely rare. You can't have more than 1 N.E. Prinny in your inventory. When you get one, use it to strengthen one of your heroes.
N.E. Prinny can sometimes show up at the Rosen Queen store - you buy them with Nether Quartz. You can also get it during events or as a reward for completed missions.