The goldfish is a popular aquarium pet. However, they have slightly different water requirements from most other aquarium pets and require lower temperatures. However, there are several options if you want to find a tankmate for your goldie.
The standard answer to this question is that goldfish should only be kept with other goldfish. However, you need to make sure you have plenty of room (30 gallons is recommended as a minimum for goldfish). Also, some ornamental goldies, like the bubble-eye goldfish, should only be kept with their own breed, as they have trouble competing with other goldfish for food.
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Koi are a larger relative of the goldfish. They have similar care requirements and can get along under the right circumstances. Koi generally do better in the largest of home aquariums or, better yet, ponds. You can keep goldfish and koi together as long as the koi are not large enough to eat the goldfish. Obviously, this is not a permanent arrangement.
Chinese Sailfin Sucker
The Chinese Sailfin Sucker is another fish that can work with a goldfish, but only if you have plenty of room. They are somewhat hard to come by, and they can outgrow a goldfish. They are more than three feet long as a adults, but can live with a goldfish before they're fully grown. They have similar requirements in terms of water temperature. These tank buddies also go by the name Chinese highfin suckers or Chinese high-fin banded sharks.
The hillstream loach (also known as the Hong Kong pleco or butterfly loach) is often sold as a tropical fish, but does its best in temperate water, like goldfish. Again, size can be a problem, but in this case the loach is smaller than a fully grown goldfish at only 4 inches. They also require special feedings of sinking foods, like fish pellets. They can work in a goldfish aquarium as long as the goldfish are not large enough to threaten them.