Yes, and no. While there are many two seater go karts available, they tend to be slightly different when compared to the standard go kart. They are still classified as go karts, but many tracks may not let you use them, because they are much heavier, because they have a larger engine, and therefore may give you an unfair advantage against other racers.
Many popular tracks do offer passenger rides in their two-seater go karts, which are often faster, and can make for an exhilarating experience. If you would prefer to take a friend or your child out for a spin in a two-seater kart, make sure to contact the track in advance to ensure that this is okay. Many tracks may not allow this, or may only allow it outside of peak hours, so do not risk just turning up, as you may be disappointed.
Some popular go karts can even have sidecars attached, which make the vehicle a little wider, but do add an extra seat nonetheless. Some go karts have two seats side by side, as you would in a car, and some may even have the passenger seated behind the driver. This is all down to personal preference, as some people prefer a longer, thinner go kart, whereas many prefer a wider, shorter go kart.
If you are looking for maximum speed, then your best bet is to seat the passenger behind the driver. This will allow you to get much better aerodynamics, as the whole vehicle is thinner, and the air resistance significantly lower, allowing you to accelerate much faster, giving you the edge over the competition.