Can multiple similar planets share the same orbit without interfering with each other too much?

Let's go with an example. Three planets, all of roughly earth's size, follow the same orbit around a star with a mass of roughly 1 sun. Basically, all three planets are almost identical to Earth, orbiting a star almost identical to our sun, at an orbit almost identical to Earth's. How plausible is this, and in which ways would the planets interfere with each other, assuming they all orbit with the same velocity?

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Can multiple similar planets share the same orbit without interfering with each other too much?

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