I have heard several cases of Serpae Tetras being very aggressive toward tankmates. In some cases that I have experienced the Serpaes being aggressive, it was mainly because of lack of space and swimming room to themselves due to overcrowding. Also, the more Serpaes you have, the more territorial they become.
I had a group of 5 Serpae Tetras that fin nipped everything in the tank. I had to get rid of them after they killed two of my Clown Loaches and a couple of Molly Fry. They are very pretty Tetras, but I would say keep them in a larger group than 5, and with very short finned tankmates.
I had four Serpaes that I used to cycle a 80 liter tank and then added two giant danios, a dwarf gourami, and a lyretail sword. As soon as I put the other fish in, the smallest serpae started attacking the lyretail and gourami and nipped their fins. I removed this one fish and the other, bigger serpaes seem to be doing alright with the other fish. The serpaes I have seem to be always chasing each other but they don't do very much damage. In the store where I got them, the long finned serpaes were labeled as semi-aggressive but the shorter finned ones (like the picture above) were labeled as docile.
I have 9 Serpae Tetras in a 150 liter tank with 4 Julli Corys, 2 Striated Loaches, and a Clown Pleco. They have never shown agressive behavior towards any except themselves, but with no real injuries. Then I added 10 neon Tetras. Within 5 days the Serpaes had killed them all. I have recently added 7 Lemon Tetras and have not noticed any problems.
I started my 180 liter tank with 6 tetras, 3 black and 3 serpaes. Both the black and serpaes tend to stay to themselves, and not quarrel or fight with each other. For the most part my serpaes are well behaved and peaceful - until I introduced 2 small, friendly catfish. The black tetras couldn't care less, but the the serpeas picked at, and stalked my newely introduced catfish. After a couple of days the catfish (I guess) felt right at home, and started to play in the tank, swim up and down, etc, and my catfish would just run into the serpaes! The serpaes now move out of the way! They no longer bother the catfish.
I had 3 serpaes in a 40 L tank along with a black molly that totally harrassed them. So I moved the serpaes to my 110 L tank where they are very happy. One of the serpaes seems to have an area of its own and chases the other two away. They seem to get along good with all the other fish.