Yes you can do this, simply name the extra ships how you wish. For me I tend to have pictures I already have in mind that will be a destroyer or cruiser etc, I then just name them cruiser 2, 3, 4 etc. Then when you are designing a ship in the game click the drop down arrow next to the ships picture, this lets you then pick a picture to use for you design. It is not just limited to your own race family, you could for example scroll down and decide you wanted your new mining base to use the picture of a Shakturi cruiser, or the planet destroyer ship. The game doesn't care as it is simply a graphic and it will scale it accordingly. The main reason for putting ship pictures in your race family folder is just for ease of organising things, as it means the extra ship pictures will show up in the same group as your race family ones.
The one limit to this I believe is the AI makes zero use of this, so even if you gave them 20 different frigate pictures they will always design ships using the standard "frigate.png" picture.