Throughout the story, Venom turns out to be the most complex and interesting character. He realizes he has to join Spider-man to bring down Carnage, but he doesn't have to like it. The two argue constantly over how to best handle the situation, with Spider-man trying to hold on to his morality while Venom argues that the only way to prevent the deaths of thousands is to kill Carnage and his cohorts. At one point his overzealous encouragement for Firestar to cook Carnage alive with her fire powers turns her back at the last minute, afraid of becoming a killer herself.
At the very end, the good guys do manage to find a way to stop Carnage without having to kill anyone, but the solution is so utterly inane that I have no idea how they intend this to be used as a moral lesson for the readers.
Below I have outlined the plot of the 14 issues of Maximum Carnage. If you would like to avoid the spoilers, skip to the bottom.
Spider-Man Unlimited #1: Carnage Rising! (written by Tom DeFalco)
Cletus Kasady is being held at a maximum-security facility for the criminally insane to be studied, I guess after being defeated by Spider-man and Venom in his previous appearance. He's given the full "Hannibal Lecter" treatment to prevent him from hurting anybody, strapped to a hand truck and almost completely immobilized. When they try to take a blood sample, the Carnage symbiote (which lives in his bloodstream) is released, and he slaughters his way out of the institution, freeing another inmate (Shriek) along the way after finding that she was enjoying the killing. The pair run across Spider-man's Doppleganger from the Infinity War and Shriek and Doppleganger crack one of Spider-man's ribs while Carnage sets a trap to lure Venom back to New York and get his revenge.
Web of Spider-Man #101: Dark Light (Terry Kavanagh)
The hero duo Cloak and Dagger join Spider-man in the fight, but Shriek destroys Dagger's body completely in the battle. Carnage gets back from the Daily Bugle, where he set his trap for Venom, but pulls his team out of combat to berate them for attacking Spider-man without him. Cloak is devastated by the loss of his partner Dagger.
Meanwhile Venom, in San Francisco, California (I think due to a truce with Spider-man where he agreed to leave New York and they would leave each other alone?), sees the news report Carnage forced the Daily Bugle to make and heads back to New York.
Amazing Spider-Man, vol. 1 #378: Demons on Broadway (David Michelinie)
Carnage has "family" problems with keeping Shriek and Doppleganger under control while Peter Parker has trouble himself with Mary Jane, upset that he has to risk his life as Spider-man all the time. Carnage beats his family into submission but Peter has more trouble dealing with Mary Jane his way.
Demogoblin (who has teamed with the Doppleganger before) is attracted by the violence and makes his first appearance in a skirmish with Spider-man, he'll join the Carnage family a bit later. Venom shows up in New York and tracks down Carnage while he's killing people, but is no match for Carnage, Doppleganger, and Shriek together and drags his broken, defeated body to the Parker apartment for help.
Spider-Man, vol. 1 #35: Team Venom (David Michelinie)
Back at the Spider-lair (okay, studio apartment), Venom proposes a truce with Spider-man to stop Carnage, then falls asleep to rest and recuperate. Mary Jane can't stand to be in the same room with the killer so she runs off in a huff to Aunt May's. Spider-man, unsure whether to team up with his enemy, asks Black Cat for advice. She heartily endorses stopping Carnage at any cost and joins the team herself. Spider-man, however, decides to enforce some rules and absolutely forbids anybody on his team from killing anybody, even Carnage.
Demogoblin meanwhile joins the Carnage family (regrouping at an old warehouse Shriek used to frequent), since they could help his quest of purging the Earth of sinners (i.e. everybody).
Cloak, in a fury over what Shriek did to his partner Dagger, jumps the gun and attacks the Carnage Family in the warehouse, but Team Venom shows up just in time to lend a hand. The battle is too balanced for a conclusion here, though, and Carnage decides to split so they can get back to killing people, causing a distraction by burning and collapsing the warehouse, incapacitating Venom (fire) and Black Cat (rubble) in the process.
Spectacular Spider-Man #201 (J.M. DeMateis)
Spider-man refuses to give chase to the fleeing Carnage family and stays behind to help Venom and Black Cat instead. This isn't a popular decision, as both Venom and Black Cat think he should have gone after Carnage. Spider-man can't play by Venom's rules and breaks the team up, but Black Cat and Cloak decide to follow Venom since the most important thing, they think, is stopping Carnage at any cost.
Spider-man wrestles with his conscience as Carnage wrestles with Demogoblin over whether they should have a plan or just randomly run around killing everyone they see. Carnage and his philosophy of chaos wins and the slaughter begins again. Spider-man has to deal with a riot and winds up on the verge of discarding his values as a result.
Web of Spider-Man #102: Sinking Fast (Terry Kavanagh)
Venom decides that he needs to bring some of Marvel's more notorious anti-heroes along in order to stop Carnage, since traditional heroes like Spider-man aren't being effective, and they hire on Morbius, the living Vampire. Team Venom shortly catches up with the Carnage Family slaughtering a dance club and the fight starts again: Venom, Black Cat, Morbius, and Cloak against Carnage, Shriek, Demogoblin, and Doppleganger. Neither side is working effectively as team, however, and it's going nowhere until Spider-man shows up and tips the odds to Team Venom. The Carnage Family sets the club on fire to escape, and everyone is ready to give chase, but Spider-man says they owe him for showing up and he gets the team to save the survivors in the club before heading out again.
Spider-man rejoins Team Venom, but this time it's Venom who makes the demands. Spider-man can't let his rigid morality interfere with stopping Carnage if he wants to stay on the team.
Amazing Spider-Man, vol. 1 #379: The Gathering Storm (David Michelinie)
Cloak uses his teleportation powers to search the city while Team Venom stops another riot. Things are getting so bad that even Aunt May is starting to question her value system. Meanwhile the living vampire Morbius heads out to gather some information on Shriek, since nobody knows who she is or what all she can do, but has to wait before giving the information to the others since daybreak is coming.
Demogoblin expresses impatience as the Carnage Family takes a break from slaughter to vandalize a museum, but Carnage delights in destruction of all kinds. The NYPD Extreme Emergency Team (S.W.A.T. Team with bigger guns) shows up to get slaughtered and ends the tension between them, and Carrion joins the Carnage Family during the fight. No reason is ever really given.
Team Venom heads off to the Fantastic Four's headquarters, which I think is still under repair from having its top blown off during the Infinity War. The Four aren't home, so they need to break in to "borrow" a sonic weapon Mr. Fantastic invented, since the symbiotes are known to be vulnerable to flame and sonic attacks. While that's going on, Deathlok shows up and actually does some decent damage to the Carnage Family before getting knocked into a neon sign, taking him out of commission.
Spider-Man, vol. 1 #36: Hate Is in the Air (Terry Kavanagh)
Taking a page from Carnage's playbook, Team Venom gets the Daily Bugle to publish a trap for Carnage this time, luring him back to the orphanage where he spent the tortured and mistreated youth that turned him into a psychopathic monster. This really just served to add some exposition and flesh out his character a little (very little), but it provides yet another battle between Team Venom and the Carnage Family.
Team Venom, with their newest recruit Firestar, bursts in to the Orphanage for another showdown. When the sun goes down, Morbius shows up to join the battle as well. Firestar and Venom use a two-pronged assault of fire and sonic blasts (although it turns out Carnage has become immune to sonic attacks) to burn the symbiote right off of Carnage, but Spider-man stops Venom just before he kills the helpless, powerless Cletus Kasady. Shriek uses the interruption to cut Kasady's face with her fingernails, and the symbiote re-emerges from his bloodstream to reform Carnage.
Spectacular Spider-Man #202: The Turning Point (J.M. DeMateis)
The battle continues, with the situation getting complicated by another riot. Spider-man and Firestar have trouble being teammates with Venom, Morbius, and the enraged Cloak, and Black Cat is trying as hard as she can to draw a line between getting as vicious as necessary with the Carnage Family and trying to keep innocent people from getting hurt.
Firestar gets Carnage in her sights again and manages to incapacitate him with her heat blasts, this time intending to finish it. But encouragement from Venom makes her realize what she's doing and she stops before killing him. Venom attacks Firestar for not killing Carnage, but Spider-man interrupts, and Venom literally knocks him over the horizon for his trouble. With the good guys turned on each other, Shriek uses her sonic blasts to take Venom (who is still vulnerable to sonic attacks) out of action, and Carnage and Shriek bring him to the Statue of Liberty for some torture.
Captain America then shows up to offer his help.
Web of Spider-Man #103: Sin City (Terry Kavanagh)
The "good guys" wind up split into the traditional heroes (Team Spider-man) and the anti-heroes (Team Venom) as Black Cat, Cloak, Morbius, and some B-list hero called Nightwatch run off to save Venom while Captain America, Spider-man, Firestar, Deathlok, and Iron Fist try to calm down the riots.
Black Cat, not actually having any superpowers, decides that she's way out of her league here and goes home before she gets killed. Cloak also decides to take a break from the fighting since he isn't getting much accomplished either.
Amazing Spider-Man #380: Soldiers of Hope (David Michelinie)
While Venom is getting tortured in the background, the sun comes up and Morbius has to flee the battle with the Carnage Family. Without him Nightwatch can't fight on all by himself so he flies off with a rapidly-weakening Morbius, leaving Venom alone again as Team Venom has now completely disbanded. Morbius and Nightwatch essentially drop out of the series at this point.
The traditional heroes find out Shriek is the cause of the riots with some kind of power she has to incite violence with her sonic powers. They manage to use their reputations to calm down huge areas of New York by their noble example, but Shriek turns up the volume and it starts all over again.
Spider-Man, vol. 1 #37: The Light (J.M. DeMateis)
Team Spider-man is still trying to stop the rioting while Venom finally escapes from Carnage. Hiding a bit of his symbiote in the sonic weapon he stole from the Fantastic Four, he tricks Carnage into shooting him which only serves to restore the symbiote to him completely, allowing him to break free.
Carnage is a little upset with Shriek for running off to go killing without him, but as he begins to punish her Doppleganger tries to protect her. Carnage kills the Doppleganger for rebelling against him, which comes close to prompting Demogoblin to leave this chaos as it is only hindering his mission.
However, with Shriek distracted, the good guys managed to disperse the riot and close in for what is finally, the final confrontation between Team Spider-man and the Carnage Family. Just before they come to blows, however, Cloak teleports back in... with Dagger.
Spectacular Spider-Man #203: War of the Heart (J.M. DeMateis)
Death rarely takes in comic books. Dagger's body was just transformed into light and scattered, but she managed to somehow contain herself in Cloak's cape until she could reform. Everyone else stops to watch as she confronts Shriek, which must be very therapeutic for her. Not many people get to confront their own killer. Dagger wins, but when she tries to user her healing powers to heal Shriek's tortured mind and offer her forgiveness, Shriek rejects the offer and attacks again.
After a brief conversation whereby the Carnage Family gets its affairs back in order, they turn around to find that Team Spider-man took a hike, leaving only Spider-man himself behind. He engages the Carnage Family (minus, fortunately, Doppleganger, who he had the most trouble with) single-handedly for a while, barely holding his own, when it is revealed he was just a delaying tactic.
While Spider-man was keeping everyone else busy, the rest of them took a ten minute breather to invent and build the most ridiculous plot device ever constructed: The Alpha Magni-Illuminator. It acts as the opposite of Shriek's riot-inducing powers to broadcast good feelings and positive emotions, which takes down the entire Carnage Family and somehow transforms Carrion back into a normal human being.
After it's all over, the Carnage symbiote is found half-draped over a lifeless body. Captain America believes his refusal to accept the positive effects of their new toy was what killed him.
Spider-Man Unlimited #2: The Hatred, the Horror, & the Hero! (Tom DeFalco)
After everyone else heads out to deal with the fallen villains, Venom shows up, angry with Spider-man for taking the glory of defeating Carnage from him, but Surprise! Carnage faked his death by putting some of his costume over one of his victims and waited until the rest of Team Spider-man ran off before showing himself.
And so finally, the final final battle starts between Carnage, Venom, and Spider-man.
Vemon and Carnage start brutally beating each other into a bloody pulp but, between his cracked rib and the pounding he took at the end of last issue, Spider-man can't keep up. Carnage is still suffering the effects of the deus ex machina from earlier and the ghosts of his past are haunting him through his fight with Venom. He manages to stay one step ahead of Venom for a while, but when he pauses to dig up the grave of his mother Venom and Spider-man catch up, and are soon joined by Black Cat.
It finally ends when Venom dive-tackles Carnage into an electrical substation, and the resulting explosion burns off the Carnage symbiote again. Unconscious and without help, he can't reform the costume, and is hauled off by the Avengers, who sure took their own sweet time getting here.
So what was the point of all this? The idea that heroes can't stoop to the level of the villains is all honorable and stuff, but when the bad guys are slaughtering innocents by the dozens and the only thing keeping the heroes from stopping them is the threat of a guilty conscience, aren't they guilty by inaction? Wasn't this what made Spider-man pick up the vigilante mask in the first place, when his own inaction resulted in the murder of his Uncle Ben? It's one thing to save a few people from a burning nightclub, but when the perpetrators have run off to kill ten times that many while you're busy doing that, what exactly have you accomplished beyond saving the people you can see immediately at the expense of those who are dying out of sight? And during the riot scenes, the heroes spent so much time dealing with the symptoms that they failed to effectively address the disease.