The first sort-of joke in Admission is actual Harvard alumnus Wallace Shawn playing Princeton’s dean of admissions, wielding a freshly published best-colleges guide and deciding that a slip in rank from number one to number two is grounds for his retirement. Ah, well, how droll.

Plot-wise, this could be a promotion opportunity for one Portia Nathan, played by Tina Fey as a prim woman who by now is starting to seem like an admissions-office lifer anyway. All that stands in Portia’s way toward deandom is a rival colleague (Gloria Reuben) with the same goal, and of course Portia’s own unawareness of how unfulfilled she really is. Pointedly childless, she has Michael Sheen for a tenure-track-professor boyfriend who pets her like a dog and reads Chaucer aloud in bed, another of those sort-of jokes, but soon enough he’s more or less lost to a lazy subplot anyway.

But Portia gets to work, making her recruitment rounds at high schools. And unlike all the eager young dynamos in the usual preparatory feeder schools, students at the alternative Quest School — where all the buildings look like starchitect-designed sustainable treehouses, and Paul Rudd teaches a third-world development practicum — tend to greet Portia with bemusement, saying things like, “Princeton is a corporation, no different than an oil company,” or “I’ll tell you what I’d like to know: Why should I apply?” One student, however, cleverly inquires about her Shakespeare-heroine namesake and makes a slightly odd but generally good impression. This is Rudd’s star pupil, played with very plausible eccentric smarts by Nat Wolff. And what follows is somehow a romantic comedy, between two other people, about whether or not he’s Princeton material.

There’s more, plot-wise, but theoretically it’s best not to give it all away. So, what to say? Did we mention Portia’s childlessness? Well, the movie does, also dwelling awkwardly on the idea that her career stability is a kind of stasis. Not that moving around a lot would be any better: Rudd’s character, having made a life of humanitarian travel to forsaken places, once adopted an African boy who now yearns for rootedness and a little bit of undivided parental attention.

Speaking of being a parent — which, again, Portia isn’t — Lily Tomlin plays her mom, a feminist scholar much admired in rarified academic circles for a book she wrote called The Masculine Myth. So now we have a rom-com, a sort of parable about one unconventional young genius’ quest to penetrate America’s exclusive higher education system, and, most excitingly, a chance to behold Tina Fey and Lily Tomlin on screen together, pluckily working their way through what Tomlin’s character calls “all this mother-daughter role playing crap.” Regrettably, it turns out just to be another of those lazy subplots.

Given the movie’s title and its milieu, a raging satire would been a brave and interesting alternative, but Karen Croner’s script, from Jean Hanff Korelitz’s novel, didn’t seem to allow it. Not that director Paul Weitz, most recently of Little Fockers and Being Flynn, would go there anyway. And of course ruthless contempt really wouldn’t be right for Fey, who’s so winningly immune to its chill; nor for Rudd, who can show a vicious streak but seems lately to have played up his own warm-fuzzies in order to ascend in Hollywood. Together they seem a little stranded in a movie which, if we’re really making decisions based on merit here, doesn’t quite deserve them. If anything it highlights the limits of their respective ranges.

As romantic and comedic and dramatic and parental complications ensue, false notes tend to ring out from Portia’s predicament. For one thing, it’s like: Oh, cut it out, Admission; she’s not 37. You’d be better off just not mentioning a number there, or not insulting everybody’s intelligence by pretending. But there are, too, some right-seeming small details, like the quaint yet oppressive smugness of ivy league a cappella groups. And Weitz does at least allow us a chance to behold the admissions team fielding student and parent reactions to their decisions, including rejoinders such as “I hope you get rectal cancer.”

If Admission teaches us anything, it’s that movies can be like universities: Some are hard to get into.