Dirimens copulatio is term used in rhetoric, although the exact meaning changes depending on who you ask. The English translation is 'separating combination', and it indicates that you are adding something on to your argument.
In the classical sense, dirimens copulatio refers to a form of argument in which one introduces both an argument and an alternative argument -- perhaps even a counterargument. This form of argument, according to Protagoras and Aristotle, helps the speaker arrive at the truth, recognizing that every issue has two sides, and ensuring that each side was considered. Examples of this might include:
"I am not surprised that so many migrants wish to improve their lifestyle by moving to the UK. It is a tribute to my country that they wish to do so. And, if the numbers can be absorbed, we welcome them. But the sheer scale of the influx has put strains on our health, welfare, housing and education services that we struggle to meet – and has held down wages for many of the poorest members of our society." -- John Major
"Perhaps travel cannot prevent bigotry, but by demonstrating that all peoples cry, laugh, eat, worry, and die, it can introduce the idea that if we try and understand each other, we may even become friends." -- Maya Angelou
As you can see, in many cases the consideration of the opposing view might be brief and quickly dismissed. If you are serious in your inspection of both side of the argument, you might prefer to refer to your rhetorical frame as in utrumque partes ('on either side'), indicating that you are fairly serious in your presentation and consideration of counterarguments.
These days, you are more likely to find dirimens copulatio used to refer to any addition to an argument -- not just "on the other hand", but also "but wait, there's more!". A quick Google search gives these examples listed as choice examples of dirimens copulatio (in the modern sense):
"Remember not only to say the right thing in the right place, but far more difficult still, to leave unsaid the wrong thing at the tempting moment." -- Benjamin Franklin
"This poor girl shouldn't just tell that guy to go jump in a lake, she ought to slash all four of his car tires.." -- Jodi Picoult, House Rules.
In these cases, dirimens copulatio isn't a tool to help us find the truth, but only a flourish that may, the author hopes, encourage people to register what they say. Which, quite frankly, is much more useful in most cases.