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I think you are limiting yourself to the "Show Me" chart options, which build charts for you based on the types of dimensions and measures you select.
You can build charts without using "Show Me", by placing dimensions and measures on the rows/columns shelves as well as the color/size/text shelves. Here is an example built by placing a discrete dimension on Columns, a continuous measure on Rows, and a discrete dimension on the Color Shelf. Then choose the "Line" mark type (circled here in red)
I asked the same question a few weeks ago, and was helped by a fellow forum member, so I'm passing it on.