Continue trying therapy, but -- if this is a recent change that's taken place over the past year or so -- also realize that eight is an age when MANY kids go through a phase when their emotions run very hot and strong -- feeling slighted or insulted over what seems to be nothing; bursting into tears for no reason that's apparent to an adult; being super-sensitive (which could include being sensitive about their possessions and not wanting to share). I promise you, my daugher went through a milder version of it(minus the sharing issues) and so did the kids of many of my friends with both boys and girls the same age. One mom did some research and found that around age eight, the early round of kids' hormones are kicking in and they have less control over their emotions and reactions for a long while, plus they are at an age when they are really starting to navigate relationships and figure out where they stand -- and that includes sibling and parent-child relationships. All this contributes to a tough year between about seven and nine. The fact that your son does great at school is actually a very good sign; it means he is able to corral his feelings when he most needs to do so -- in front of others, in a group situation -- and the fact he is frustrated and not making sense at home may mean his emotions are coming out there after being held in at school.
It's important NOT to take things personally when he comes to you yelling about something; it's not you, and it's probably not him being just plain naughty; he may be overwhelmed. But I bet if you ask him, "Tell me what's wrong, tell me what's going on, tell me why you feel so mad/sad/possessive," he probably will say "I don't know!" and stamp off. Again -- I've seen it with kids who were before this, and are after it, great, sensible kids.
I might talk to a therapist or counselor without him present. Ask if his behavior really warrants therapy, or if he just is plunged in a stage that you all must get through. Yes, you will need to discipline him at times because he will do things that cannot be accepted, but also don't overreact or give too much attention or emphasis to things if you can help it -- choose battles carefully because in some cases he may feel that he doesn't know, himself, what's going on in his own head and with his own emotions, and that is scaring him, so he acts worse out of anger at not understanding his wild feelings.
By the way: If you find yourself saying, "His twin sister doesn't act this way and she's the same age so it must be him, he must be having behavior issues and this isn't a phase," reconsider that. The difference in gender could play a part of it. And never compare one child's behavior to another's just because they're siblings -- even twins. Again, I'd really talk to a professional about it -- without him there.
Meanwhile, stop throwing other kids into the mix since that's a problem. Reduce the problem for now by not having other kids over as often, or limiting things to kids you know he knows well, and keep the play dates short. It might also help to have specific activities arranged rather than letting them free play as much with his toys -- take them to a movie and for pizza; take them to a park; to laser tag once in a while; etc. Something where they are focused together on an activity other than playing with toys.This reduces the chances of a fuss over the toys and increases the chance of a positive interaction because your son will be, well, outside his own head and emotions for a while.