Find an equation with different commonness behavior across numbers of colors

Construct a linear equation that is r-uncommon for some integer r at least 3 but s-common for some integer s less than r.

Background

The paper asks whether commonness can depend non-monotonically on the number of colors. Its main implication establishes monotonicity from 2-uncommonness to r-uncommonness for larger numbers of colors, but it does not settle whether an equation can be uncommon for one number of colors while common for a smaller number. The question is especially relevant for equations with a canceling partition that are 2-common over the integers, a class the paper describes as poorly understood.