A young child's life is pretty constantly managed, and often abruptly manipulated, limited and controlled by parents and caretakers, schedules and circumstances.
Some children can accept all this management without too much distress. Some find it incredibly frustrating. Too much frustration (which the child did not choose to feel) quite logically results in either tantrums or withdrawal. In the case of tantrums, parents may believe it necessary to add an additional frustrating layer of discipline, which usually translates as "punishment."
You don't say what kind of situations result in your son's blowups, but since that behavior seldom occurs without some situation that provokes it, can I assume that he is often reacting to your requests, demands, rules and restrictions?
If that's the case, can you consider life from his perspective? There may be ways you can reduce the conflict and clashes by simplifying his days, planning ahead when you need to meet a schedule, giving him advance notice when he'll need to let go of an activity he's enjoying, participate cheerfully with him when you want him to complete a task (probably won't take any more time than dealing with a tantrum), and keep as much humor and fun in your days as possible (this will enrich your parenting experience, too!).
Going on 4, he's old enough for you to talk to him about the purpose of / need for discipline. Explain that if he can control some of his own behavior, he'll get to avoid punishments, time-outs, and a lot of frustration. Point out that you will make every effort to make his life easier and happier, and that you need the same effort from him. You probably already do that, but he'll also need a specific time period to actually experience the truth of it.
Ask him what would make his life easier (his answers might even surprise you if you help him narrow and refine his answer.) Tell him one thing that would make your life easier. Ask him to try it for just two or three hours and see how much better all of you feel. If he connects with that, celebrate even a couple hours' improvement by doing something with him that he'll just love.
You will probably be pleasantly surprised. Kids are remarkably perceptive, and even though impulsivity is the norm and self-control is hard to come by at this age, short periods of mutual cooperation and appreciation are possible. It can almost become a game, and games are very appealing to children. (Do allow for the fact that your twins are still very, very young, and will not have much sustained self-control for quite a few years yet.)
Except for those occasional kids who are truly challenged by emotional disorders, children truly do want to be happy. Even the most negative behavior is actually a mistaken strategy to find greater happiness.
But kids need help understanding that, and often need better alternatives modeled by someone with more experience with life – like a loving parent. Almost every child can be drawn slowly into patterns that will make the whole family happier. This requires awareness and attention by the adults in his life, and sometimes retraining of habits even the best-intentioned parents can so easily fall into.
Good luck! I predict a more peaceful family in your near future.