Well, redfoot tortoises and pancake tortoises are known to live in groups. Keeping them is, however, a bit more advanced. They have specific requirements. Leopard tortoises and Indian Star tortoises can live in groups, but sometimes the males fight. Radiata do ok with others of their kind, but are very expensive! I would consider Leos and Indian Star tortoises more advanced torts as far as care. There is a narrower margin for error. The only tortoise in the testudo species that seems to do ok in groups are Marginata, but they are also quite large as adults.
Generally, torts don't like to be together... But there are some exceptions like @biochemnerd808 said
Unless it is absolutely necessary, tortoises do better alone. Less stress.. no bullying.. all that space to themselves.
Box turtles are generally more peaceful together, though. Keep in mind that successful groups in any species are dependent on individual personalities, space/resources (i.e. multiple water dishes, etc.), and gender ratios. For most species, 1 male to 2-4 females is ideal.
You also have to make sure you can realistically be able to house multiple tortoises whether they're together (by providing a really large enclosure) or, if need be, separated (several large enclosures).
I have 3 redfoots together in a large outdoor enlcosure. 1 male, 2 females. I also have 3 hide boxes and the male does not normally sleep where the female sleeps. It pretty common for my two females to share a hide box but often they all stay in seperate hide boxes and keep to themselves.