Shrimp and gobies should be ok but might get attacked when the anemonefish breed. However, if you only have 1 anemonefish, it won't breed and shrimp and gobies should be fine.Would I be able to keep other species in that same tank as well? (Say maybe a goby or shrimp?)
If you only have 1 anemonefish, it will turn into a female and should you choose to add another, you will need a juvenile so it becomes a male.
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You move marine tanks like any other tank. Take all the rocks out and put them in a bucket. Put the fish in buckets with the tank water. Empty the tank and move it, then set it back up.