Ideally just one officer is needed to apprehend and move someone under arrest. The officer will use handcuffs on the wrists to prevent being punched. Compliance is achieved by force if necessary with the use of striking, a club, or a taser.
But of course that's not easy when the person under arrest is physically much stronger or heavier and is putting up a fight. So, more than one officer may be needed to gain control.
In the case where 4 officers were needed, one for each limb, I've seen that happen in three different situations. First situation is when the one they're arresting is high on something like PCP and is unusually strong and energetic. They're actually out of their minds when they're like this and see the officers as trying to kill them. You can't even hold their arms close enough together to place them in handcuffs. This happens with doctors in hospitals, too. It might take 4 nurses to subdue someone who's freaking out due to an adverse reaction to a sedative or something, long enough to inject them with something that knocks them out. And it requires all their body weight placed on each limb, believe it or not.
The second situation I've seen come up is when there are no handcuffs available, and nothing to bind wrists and legs. Some people comply and go along with the officers regardless. But you need more than one officer when they're resisting.
The third situation happens probably the most. That's when you have a riot or a protest with lots of people that need to be arrested all at once. The officers will just gang up on one of them and physically carry them off to a van where they are detained. Then they go back and get the next one, and the next one, etc. It's quicker and safer to do that, rather than having a single officer struggling to place them in handcuffs. There's probably not enough handcuffs in these situations as well. And the ones that really resist and refuse to walk are the ones that need 4 officers sometimes.
As for whether or not this can be improved and only use one or two officers, yes of course there are more efficient ways. The use of handcuffs and tasers to gain compliance is the primary way of apprehending someone. Then you need less officers. Using pepper spray or tear gas is something else you see. People sometimes just need time to calm down and for officers to calm them down with their voice and deescalate the situation. That's effective, too.
If you're asking because you want to know if there are special techniques or maybe pressure points that can be applied from martial arts, you're mostly out of luck. In a book you're writing, sure. In reality, not so much.
But if your main character knows martial arts, I'd say one of the more interesting and applicable martial arts to look at is Bujinkan Budo (also known as ninjutsu). They have training in rope binding (hojo jutsu), which you can sometimes see in movies. Pressure points are integrated into all of what they do. They typically flip someone over onto their stomach using leverage on one of their outstretched arms and then press down using their knee onto a pressure point on their back under the shoulder blade where it causes breathing to become painful and difficult. At this point, it's difficult for someone to move. They enforce compliance by then twisting at the wrist, elbow, or shoulder. Or they might press into a pressure point behind the ear or grab a hold of the neck as a way of saying they can squeeze and snap the windpipe if they move. With rope binding techniques, they may take someone down using the rope, and then tie up their arms, ankles, and then both arms and ankles together, along with the neck. They basically get "hog tied" Japanese style. Everyone training in Bujinkan is taught how to quickly fashion handcuffs from rope, and then they integrate the rope binding technique with their taijutsu. It originally came from one of the 6 traditional samurai ryu that Bujinkan incorporates. Fascinating stuff. And the idea is that when the ropes are put on, any struggling will actually cause pain to the one struggling. Essentially, they're just fighting themselves at that point. Then it becomes easy to take them away. Sometimes I see Bujinkan teaching to slide a staff through the rope binding, and two people carry him away, one on each side of the staff.
Hope that helps.