Dungeons & Dragons has a general principle that specific rules override general rules (see page 7 of the Player's Handbook and the introduction to the Basic Rules). That means that if the designer of a magic item wants it to take up two attunement slots on a character, they can have the specific rules for that item override the the general rules that say that you can attune up to three different items.
An example of this general idea (that a specific rule can modify the general attunement rules) already exists, as the Artificer class published in the recent Eberron books (though not the Unearthed Arcana playtest version). An Artificer gets extra attunement slots at levels 10, 14 and 18.
There are probably a few different ways a rule to require double attunement could be phrased. The item could simply say that it counts as two items for attunement:
This item requires attunement twice before its magical properties apply. It counts as two attuned items for a character who attunes to it twice.
Or it could modify the rules about how many items the attuning character can attune to at the same time (while only taking up one slot itself):
This item requires attunement. While attuned to this item, the number of items you may be attuned to is decreased by one (usually from three to two). If this reduction would mean you would be attuned to too many items, your attempt to attune to this item will fail.
Of course, that phrasing assumes that the item is beneficial to the wielder, and that the extra attunement slot cost is a trade off for some really good positive effects. If it's a cursed item however, there could be other ways to phrase the magical effects that are more explicitly bad:
Curse: When you attune to this item, the number of items you may be attuned to is decreased by one (usually from three to two). If this reduction means you would be attuned to too many items, your attunement to one of your other items ends immediately. You may choose which item loses attunement, though this effect will not break any other curses. You may not remove or end your attunement to this item until you are targeted by Remove Curse or similar magic.
All of these examples are just things I made up. It may be that no official item published by Wizards of the Coast will ever monkey with attunement the way I have suggested. But that doesn't mean you can't do so for your own game. As long as the rule makes sense to you and the other players at your table, there's no reason not to include it if you think it would be fun.