The general rule is 2 boxes per cat, plus one, or 1 box per cat plus one as the minimum. And cats prefer having two boxes to use, one for pooping and one for peeing. I guess some people have observed some cats taking a pee in one corner, and then turning around and pooping in the opposite corner far from the pee. Also, boxes should be in quiet places, never in heavily trafficked or chaotic areas. And they hate having to eat/drink near their box (same with dogs and their potty areas). When it comes to litterbox habits, it's never a bad thing to go above and beyond to keep the kitty happy, I think. Of all the things in a cat's life, the box should be #1 for the human, unless they don't worry so much about accidents, lol
But it's also possible that whoever's having the accidents is having ouchie problems with his feet or digestion. Could be worms, as someone said, or maybe he hurt his foot somehow and the litter gives him pain when he uses it. If the cat is in any discomfort while pottying in the box, he may associate it with the box and will find another place, usually soft, smooth areas (like clean laundry or smooth floors). Or maybe you changed litter brands recently and he doesn't like it (some litters are really heavy, some are light, some are stinky and dusty, some are scentless, and worst of all, some are citrus scented, of all things! Gah! I pity the kitty!) I have a girl, Willow, who frequently leaves a deposit somewhere, in a corner. We're redoing the whole upstairs of our house, where one of their boxes' is, and it was moved near the computer desk, where nearly everything was shoved when the other rooms were being sanded and painted. Far too chaotic, especially since my dog's bed was only feet away, and the box was under the computer desk, right next to human legs. When Willow started reacting to that, we moved it to the bottom of the stairs and it seems to have cleared up. But Willow always pees on purses and backpacks that have been carelessly left on the floor. If you buy something that's not washable, it's your own fault, lol (can't always blame yourself for your beloved red purse(with a couple leather patches) ending up on the floor, when someone else would shove it off the couch to make way for themself... I still mourn that purse and haven't thrown it out yet, because maybe there's a way to wash it... lol).
But whatever the reason, do NOT get rid of him. Litterbox problems are extremely common, and is a top complaint for many of the cats dumped at shelters. In fact, it's probably the most common complaint, before "we've moving," "we're having a baby," and "she doesn't match the couch." Don't dump your problem on someone else, you owe it to your kitty to help him, as since this is a sudden thing, he's uncomfortable in some way, physically or mentally.