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In Euclidean planar geometry, not unless they're collinear, in which case they intersect an infinite number of times.

In other types of geometry ... maybe.

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Q: Can three coplanar lines intersect twice?
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What is the maximum number of distinct intersections of 30 different coplanar circles?

No two circles can intersect more than twice. Each circle can intersect with each other circle. Thus there ought to be 2 × 30 × (30 - 1) intersections. However, this counts each intersection twice: once for each circle. Thus the answer is half this, giving: maximum_number_of_intersections = ½ × 2 × 30 × (30 - 1) = 30 × 29 = 870.

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