Consilience (from Latin, "leaping together") is a word coined by William Whewell to describe how different kinds of evidence "leap together" to support the same conclusion. Consilience has also been used in ethical discussions to capture the way that when an action is right for one reason, it is often right for several reasons. A couple of current examples: curb cuts were instituted for the handicapped. Their consilient benefits extend to people on bicycles, parents pushing baby carriages and folks with wheeled grocery carts. In Nebraska, several conservative legislators' reasons for abolishing the death penalty were rooted in saving money, rather than doing justice. The abolition of the death penalty accomplishes both ends.
Recognizing the property of consilience and looking for chances to put it into practice makes it possible to have much larger coalitions. Maybe you want a higher minimum wage because you see that people's time is valuable. Someone else may want it because better paid workers stimulate the economy. A third person wants a higher minimum wage because they see the food stamps and Medicare of Walmart workers as government subsidies of private business. What is overwhelmingly important here is that all of these people can work together to get a higher minimum wage.
Not only that, they are all right! It is a commonplace of mathematics that a theorem that is true will have more than one proof. The Pythagorean theorem has at least 367 proofs. All of these proofs are correct. Some may be easier to follow. Some may implicitly have wider application than other proofs. Some are more beautiful than others. Nonetheless, every valid proof is still a valid proof. If we find that we agree on a particular goal but our companion wants it for a different reason, that is no barrier to working together to reach the goal.
Once we recognize this, it becomes easier to make the cases (plural intentional) for our positions. The more that we know about the premises of another person, the more likely it is that we can find a valid reason that speaks to them. If we have open minds, we may even learn something we didn't know before.