A noted downside to keeping both koi and goldfish together. 
 
The eye-attacking behaviour of Koi fishes was recorded in a koi–goldfish polyculture system. The attacked fishes suffered from eye ablation, abnormal swimming and suppressed feeding behaviour. There was a significant difference in mean sizes of victims and attackers but the exact motivating stimuli for the observed action was not clear. For future research, the effects of different stocking ratios on aggressive behaviour of koi should also be examined.
 
Full article: Observation of the eye-attacking behaviour of Koi Cyprinus carpio var. koi in a koi–goldfish polyculture system (tandfonline.com)