An organism that feeds on many food types is called:
Euryphagous organisms consume a broad range of food types; eu-ry indicates breadth, while -phagy refers to feeding. Such generalists can switch resources when one becomes scarce, which may support survival in variable environments. A stenophagous species has a narrow diet and may depend on one prey or host type. “Omnivore” describes consumption from both plant and animal trophic sources, not necessarily broad choice within those sources: an omnivore can still specialize on a few foods. “Polyphagous” is also widely used for organisms, especially herbivorous insects, that feed on many host speci
Ref: Evolutionary Analysis, Herron & Freeman, 5th Ed., Ch. 10