Short answer: it can, but most vets and welfare groups say it shouldn't. Rabbits are social animals. In the wild they live in groups, and they spend their days grooming each other, napping side by side and keeping watch together. A single pet rabbit has to get all of that from you, and even the most devoted owner is asleep, at work or out of the room for a big part of the day.
The best company for a rabbit is another rabbit.
Rabbits talk in a language of body positions, ear angles, thumps, nudges and mutual grooming. Another rabbit speaks it fluently. We don't. The Rabbit Welfare Association & Fund says rabbits need company, and that the company should be from other rabbits. The RSPCA agrees, and adds that a rabbit and a guinea pig shouldn't share either: they have different diets and different ways of communicating, a rabbit can injure a guinea pig by accident or on purpose, and rabbits can carry bacteria that make guinea pigs ill.
There are exceptions. A vet may advise that one particular rabbit has to live alone, for example because of a health problem or because several bonding attempts have failed. If that is your situation, ask your vet and the rescue you adopted from what your rabbit needs, such as more daily time with you, more space and more things to dig and chew.
The RSPCA says a neutered male and a neutered female is usually the most straightforward match. Two neutered females or two neutered brothers can work too, but the chance of a failed bond is higher. Neutering matters for every combination, because it reduces fighting and unwanted litters, and it brings health benefits. Both rabbits need to be neutered before they meet. Your vet can tell you how long to wait after the operation.
Put in your plans below and see which step is next. The numbers come from the RSPCA and the Rabbit Welfare Association: a pair of medium-sized rabbits needs at least 3 m × 2 m × 1 m high as their permanent living space.
Bonding can take anything from a couple of hours to a couple of months, so patience is part of the job. Many rescues offer bonding help or already-bonded pairs, so check with them first.
Losing a companion is hard for the rabbit who is left, as well as for you. A single rabbit still needs rabbit company, so ask your vet or rescue how and when to introduce a new friend.