Is it possible to live healthily on a diet that is not directly or indirectly connected to the harm of living beings?

The lives of plants are generally not considered to be as important as those of animals, but they are in fact living beings. I wonder (hypothetically) whether it would be possible to exist solely on a diet composed of things which are naturally produced by plants and animals, the taking of which does not harm them?

For example, milk and eggs can be taken without harming the animals in question. Fruit can be plucked without harming the tree, and I imagine some vegetables exist that could be harvested without harming the plant.

I don’t really think I’d pursue such a diet, I’m just wondering whether it could be nutritionally viable.