I am lucky to have a large garden space and so I have the luxury of being able to dedicate some of my beds to a single perennial species.
Dianthus, alone in a small bed, can be pretty as the foliage is neat and forms a weed- suppressing mat above which the pretty, little flowers are held aloft.
I have a bed of only pure white German iris that I love for its purity and conformity. And one year my pink Japanese anemones took over a whole bed on the side of my yard, outside my fence, so I just let them have it. The foliage is neat and suffocates most of the weeds, and in bloom, that bed is a sea of pink and looks like the garden of a princess.
In some of my other beds, more by happenstance than design, I have let different but equally vigorous plants duke it out. Monarda, commonly known as bee balm, nearly engulfed the other perennials in one bed, but now when it has bloomed, I just pull it all out after a rain so the roots come out easily. There is always lots left to return the next year. The wild asters and golden rod then fill in for a fall display without any more work on my part.
Around my fountain, where the water splashes and the soil remains wet a lot, I have Japanese, Siberian and Louisiana iris that enjoy moisture. They bloom at slightly different times, which adds to the appeal, as does the fact that all of the blooms are in purple/lavender shades, and they seem to float above their clean erect foliage.