I know I read this after 2012, I think as an ebook. The cover depicted a knife switch by itself, I think closed with the handle up. At the beginning of the story, the protagonist, a boy, is told by his friend at school (another boy) about a strange house on the back of a flatbed truck in their neighborhood which they explore after school. It was a small house, like shed-sized, I think with red walls. They find the door is unlocked and inside, there's a switch, I think described as being like the ones in the cover image. I don't remember if they opened the switch, closed it, or maybe tried switching it a few times, but seemingly nothing happened before his friend find off, saying they need to get home.
The next day, the protagonist finds the world around him has changed. His family treats him in a subtly different way (I want to say that his parents got along better). His school has him enrolled in different activities. Strangest, he's friends with a bully from before, and his friend he was with the day before is afraid of him. I think he finds the house from before and tries the switch again, and winds up in an even different world where that house doesn't exist. I don't remember exactly what happens, but he winds up friends with another boy, who takes him to a homeless man (either the boy or the man had a fancy name, maybe Shakespeare based) who has talked about switches and other worlds. Said man, I think, has a respiratory illness, and he makes them a meal on a hotplate plugged into the building he's squatting in. After talking to them, the man shows them a switch in the basement of the house, which the two boys pull to go to another world.
I forget the details, but they went through several worlds. One involved a theocratic dictatorship with a guy with a fairly normal sounding name, and where they also encountered that homeless man, who didn't recognize them, but still gave some good advice. Another world was a hive mind world, I think on the shores of Lake Michigan (maybe an alternate Chicago?), and I remember they had to recover someone, and at this point they'd been joined by a girl. A later world was a tropical paradise where they found the friend from the beginning, who's served hand and foot by the natives, and who doesn't want to leave. When they try to remove said friend, the natives get violent.
Eventually, they wind up in a very alien world, I think with crystalline grass and telepathic quadrupeds, and they find a man in a building who explains the nature of the various worlds, and that he serves some purpose in keeping them all stable with the controls on front of him. He needs a replacement, and one of the kids volunteers. When he touches the controls, he rapidly ages into adulthood, I think as part of the training process, and sends them home to their original realities. After returning, the original protagonist encounters the boy who was left behind, now elderly, and I think realizes he knew him from before.
The book was in English, and might have been targeted for teenagers, as I remember there wasn't any real sex or violence.