Rats in the Cellara: All in One Volume

Each universe has its own dystopian nightmare. Some are on the brink of nuclear war, some hopelessly divided by politics, all in economic meltdown with electricity off as often as on, and police who only protect those that pay them.

Also wandering the multiverse are multiple copies of Oscar's paedophile uncle, often hunting in pairs.

And there's a cat. The cat is good.

In book one: all Oscar wants to do is find a universe where his neighbourhood isn't likely to be nuked, where he's safe from his paedophile uncle, and has a loving and stable set of parents. He also wouldn't mind living as a twin to one of his other doubles, the one they call Percy. But the cat has bigger plans...

In book two: the cat takes special interest in the one they call Louis, the bad boy. After making sure Louis makes up for some of his nastier pranks, he helps him find Blake, another instance of himself from yet another parallel universe, living in the street, a victim of two of his Paedophile uncles. The two go on a rescue mission to find the owner of their house from yet another universe, who has become lost in the network of worlds. In doing so, Louis and Blake have found a home where they're accepted as twin sons of the man they rescued. The father and two sons go on a further adventure in which they deal with the various instances of "Uncle Milton", Oscar's paedophile uncle. There are more twists and turns as they meet another creature of the same order as the cat.

In book three: the diary of Dr. James McSporran, a nuclear physicist stuck in the 18th century tells part of the story. Some unscrupulous time travellers have pre-empted the Abolition movement, turning their universe into a dark world where human rights isn't even a concept. One instance of Oscar Wild Daugherty, who becomes known as Justin, stumbles into that world, which leads to the whole group of them going in to make a difference.

In book four: the time has come to shut down the parallel worlds portal. Dr. James McSporran has arrived from the distant past to perform the task. He asks Oscar, also known as Justin, to help him. But the task is far from straightforward. On shutting it down, they are flung into the bleak world that had resulted from the evil acts of McSporran's two unscrupulous pupils. There the house lies in ruins. Switching the portal back on only resets the device, which will now only work on the original world and any that would split off from that. And split off, it does, resulting in two Oscars, and two Dr. McSporrans. At least Oscar will never be alone again, but how do they get home? The McSporrans find that two heads are better than one, but one of them must stay behind. The other takes the two boys via a make-shift time machine. Their route takes them through Victorian England, where the unthinkable happens. The two Oscars are taken away to London into child labour, while McSporran is put in prison for trespassing in his own house.

How does one get back home when locked in a silk mill in Victorian London?