Agree, but you should increase the existing tetra too. All tetra are better the larger the group, and while six is touted as "minimum" the group should always be larger than this if the tank has space, and a 60g with your indicated fish load certainly has the space for more. I would go with 9-12 Black Phantom Tetra, and get a good mix of male/female (half/half works fine).
And increase the corys (if these are corys) to five minimum; if you decide on more than the one species, three of each is OK, with 6+ total, or 9 with 3 of 3 species, etc. If your emerald cats are actually Brochis splendens, and not Corydoras aeneus, I would say five of the Emeralds will do it. This species gets a bit larger. You can still have 3 though if you want other Cory species, they get along fine. If you want to see the difference, check the profiles by clicking the shaded names.