No hard rules, but the DMG mentions the possibility
The Dungeon Master's Workshop chapter of the Dungeon Master's Guide has a Modifying an Item section describing ways a DM might tweak existing items to create new magical items for their players to discover. It states:
You can also modify an item by fusing it with properties from another item. For example, you could combine the effects of a helm of comprehending languages with those of a helm of telepathy into a single helmet. This makes the item more powerful (and probably increases its rarity), but it won’t break your game.
It does not go into any more detail than this, and there are no further guidelines about how to adjudicate the combination of certain kinds of items or how to judge the effect on an item's rarity. Nonetheless, this is clear that if you, as a DM, want to include such variant items in your game, you should certainly feel free to do so; but you're left to figure out the details by yourself.