Nagi always felt like the odd one in his family, being a diligent and ambitious learner while none of them are particularly studious. Anyway he loves them and therefore has little interest to get to know his biological parents. He gives into meeting them once, but little does he know what they have planned out for him...
"A Couple of Cookoos" constructs a hilarious setting to establish the harem plotline. The show tries to be funny, but fails to be outstandingly witty or hilarious. Its animation style is rather serious and not overly comical, which makes it hard for the show to find its place. It doesn't take itself particularly serious and therefore makes it hard to immerse or relate. It offers a certain share of fanservice while following the protagonist navigating the maze of weirdness his family, biological parents and his own feelings throw him into, but does not manage to connect to the viewer on an emotional level.
Eventually this show seems to be between the chairs. Its style does not really match with the kind of story it tries to tell, and thus fails to excel in either dimension of the romcom genre. It's still 'good' imho, but not more. Watch it if you're a fan of the genre, but leave it be if not since it is unlikely to get you hooked.