My son was like this too. He's a very smart kid, and very sweet. But sometimes he can be very moody and demanding. If you have factored out all physiological possibilities (is he tired, hungry, thirsty, overstimulated?) and you have had your fill of his demands, you can tell him so. "Hon, I need some time to myself right now, why don't you sit and play quietly?" I know this sounds like a pipe dream, but when he starts to get upset, you can simply pick him up and put him in his room, explaining "you can come out when you've calmed down and are ready to play quietly." Seems harsh, but IMO kids do need to understand that adults have needs too. In fact, everyone else has needs too! We are not meant to be slaves to our kids.
I was very against isolation for quite some time, thinking "how does this show kids how to cooperate with each other?" I had it in my mind that "time out" (which is not what we call it, and isn't really the point of it) would result in adults who would sit and stew instead of talking things out and dealing with their emotions. Well my kids aren't adults yet, but I was dead wrong. When my high-needs son starts getting out of line (becoming too demanding for my patience, or just really moody/reactive), after a warning about his behavior and how it's affecting others, I send him to his room. When he comes out (he determines when he's ready to come out, but if he starts the same behavior I send him back in again), he has usually found a solution to whatever problem was going on, or tells me that he's ready to talk about it (which is a true discussion about my observations and what he says his motivations were), and we are usually able to cooperate. Now, do understand that my son is 6, but we started around 4 and his ability to understand the impact of his behaviors has evolved over that time period.
At first, I would lead the conversations in a patient way: "when you did this what were you hoping would happen? what did your sister say when you did that?" etc. and give suggestions about how his behaviors affected the other person (or me) and give suggestions about what I would have liked. We do this with my 3 year old daughter now, and when she starts to throw a fit or get really moody she goes to lie down in her bed for a little while (without even my suggestion), then emerges a little while later either to talk about it or to simply get on with her day.
I just wanted to point out that, like adults, some kids are just more introspective than others. Sometimes they don't realize that they need to think about something or just need some quiet time alone. This was the case with my son, though I didn't really realize it until I was at my wit's end. On the other hand, it's also possible that this is just a stage for your son, and he's feeling really clingy for some developmental reason. It's also possible that there's some sort of underlying physiological or psychological reason for his behavior, or that something had changed and he hasn't come to terms with it yet. Be sure to give him lots of attention at other times, but when you're done let him know in no uncertain terms that YOU'RE DONE and it's time for you to do x,y,z.