I think if you go with too many more species of tetra, your aquarium is going to look cluttered in the midwater area. You also have tetras that are sort of incompatible with each other, IMO. Neons and rummynose are very quiet and peaceful fish, they need big schools, bigger than 6, to feel comfortable. 6 of the larger tetras should be enough, but I bet your "candy cane" tetras are going to be fin nippers. They look like bleeding hearts, black phantom and serpae tetras which are all nippy.
I might be wrong because I've actually never heard of this tetra before, but it's a real species, Hyphessobrycon sp:
http://www.thatpetplace.com/pet/prod/216128/i/7/product.web
Diamond tetras will be very active and a little nippy too. I would have personally chosen something like lemon tetras instead for this group. The smallest tetras I keep (and I too, have a 55 gallon community with tetras and kribensis) are blue tetras and silvertip tetras. I love neons and rummynoses, but I would keep them in smaller tanks in big schools. Either species makes a stunning showpiece for a 10-15 gallon tank. But they sort of get lost in a tank like this unless you make them a focal point and up their schools to a dozen each or so.
Congo tetras will be even more active than the diamond tetras, plus if there are nippy ones in your group their long fins will be like a red flag in front of a bull. They make great tankmates for fish like rainbowfish though.
My advice, skip them and go with pristella tetras maybe. Or black neons or bloodfin tetras if you like the look of them. But don't add more than one more species, and research it carefully. Tetras don't always get along so well with each other. Bleeding hearts and black skirt tetras are notoriously nippy. Very tough fish though, especially the black skirts which are cold tolerant.