I find that my relationships do affect each other, but in positive ways. Different partners show me different aspects of myself, which I am then able to apply to my other relationships.
For example, suppose Harriot is the one who interrupts Arthur, but he always lets it go. Then Harriot meets Andrew, who doesn't tolerate her interruptions. Harriot realizes what she is doing because of Andrew, and is able to apply these changes to her relationship with Arthur.
Of course, this example is overly simplistic, but when I notice that I'm behaving differently with one love versus another, whether that behavious is desirable or not, I try to figure out why and then apply the better behaviour to both relationships.