Frobisher is a penguin with attitude; he’s a shamus, a private eye, the kind of guy who’s right at home on the mean streets where you can trust no one but yourself. Or at least that’s what he tells everyone. Thus, when his old friend the Doctor returns to ask if he’s grown tired of playing detective, Frobisher is rather insulted. The office may be grimy, and Frobisher may only have found a missing cat in three weeks, while the Doctor has foiled three invasions of Earth, overthrown several corrupt dictatorships and saved the Universe twice... but at least here he’s doing things on his own, rather than just playing second fiddle to the real hero. The Doctor offers to stick around for a while until things get interesting, but Frobisher turns him away. He knows that this has hurt the Doctor’s feelings, but he must work alone. He’d rather not think about the last time he didn’t...
And that’s when she walks in: Alicia Mulholland of the Mulholland estate, a dame with a case for a hard-boiled private eye. Frobisher, gobsmacked by her beauty, listens as she explains that her fiancé, Arthur Gringrax, has been running around behind her back; she wants Frobisher to find out if he’s seeing someone else. Frobisher has been in love before, and he understands her feelings, although he can’t understand what she sees in the balding, beady-eyed Arthur -- or why such a man would cheat on a woman like her. He accepts the case, and in order to avoid drawing attention to his penguin shape, he morphs into a more inconspicuous humanoid form. As he’s never really been able to get the hang of the humanoid form, he chooses to model himself on a humanoid shape he’s familiar with -- the shape of the Doctor.
Frobisher waits for Gringrax to emerge from his place of business and follows him to a seedy motel. There, he tries to convince the receptionist to tell him where Arthur is staying, but the receptionist scoffs at his paltry bribe and says nothing -- until shots ring out upstairs. While the receptionist calls the police, Frobisher investigates the gunshots and finds Arthur’s room empty, apart from a steaming puddle of blood on the bathroom tiles. Repulsed, he examines the blood closely -- and is surprised when it seems to flinch away at his touch. Before he can investigate further, the police arrive, led by Elric Chandler (who, despite his voice, looks almost nothing like Peter Lorre). The police of this world aren’t paid to have imaginations, and Chandler thus places Frobisher under arrest; when the receptionist requests a bribe to keep quiet about these events, Chandler arrests him as well. Frobisher, wondering how Chandler got to the hotel so quickly, concludes that he must already have been watching Gringrax -- and to keep him silent, Chandler knocks him out.
Frobisher recovers to hear Chandler speaking to his employer, who demonstrates that he knows the extent of Chandler’s “loyalty” by tossing a mazuma coin at Chandler’s feet, forcing him to stoop to pick it up. Chandler leaves, and Frobisher opens his eyes to find himself in the offices of Josiah W. Dogbolter, a man/frog alien hybrid so rich and powerful that he controls slaves on a thousand worlds who don’t even know he exists. Dogbolter admits that Gringrax was his employee, and demands to know whether Frobisher found something interesting in the hotel room -- something distinctive, that might stand out. Frobisher refuses to betray his current client, even when Dogbolter points out that he can pay Frobisher twenty times what she will, and eventually Dogbolter gives up and orders his associate Elgar to take Frobisher for a ride.
Elgar drives Frobisher to the edge of a cliff, pays him 12 mazumas for his troubles, and then throws him over the edge. Frobisher morphs back into the shape of a penguin before he hits the water, and swims to shore to find the Doctor waiting. The Doctor has saved the Universe once more, and that done, has returned to ask Frobisher if he’s reconsidered. He finally admits that he’s inviting Frobisher back because he’s lonely, but Frobisher explains that he’s finally reached the point where people are trying to kill him, and the Doctor concedes that that’s the most interesting part of an adventure. He thus takes his leave again, and Frobisher transforms back into the Doctor’s shape and returns to his office to think things over.
When he arrives, he finds Alicia Mulholland ransacking his office. She tries to brush off her actions, but as she starts to leave Frobisher drops a heavy hint about Dogbolter, catching her attention. Dogbolter said “she” must be paying Frobisher a lot; how did he know Frobisher’s client was female? Alicia admits that Frobisher has seen through her, and to his surprise, she leans in and kisses him. He’s a bit out of practice, but he’s just getting into it when she tells him she loves him, and he freezes up. He doesn’t trust anyone who claims to love him -- not since his experience with Francine, who was his partner in more ways than one. At this point, Chandler arrives and threatens to kill them both unless they tell him where to find the something which Dogbolter is after. He doesn’t know what it is; all he knows is that Dogbolter fears it, and Chandler thus intends to use it against him before Dogbolter decides that he’s of no further use and disposes of him. But Alicia knows Dogbolter well enough to know that he’s probably planted a tracking device on Chandler -- and now that Chandler has led him to Alicia, he has outlived his usefulness. Panic-stricken, Chandler searches himself and finds that the mazuma coin which Dogbolter gave to him earlier is now glowing red-hot. Before he can get rid of it, it sticks to his skin, and Frobisher watches in horror as it detonates, killing Chandler but leaving the rest of the office intact.
Frobisher is shocked by Alicia’s callousness, but before he can confront her, Elgar captures them both and takes them back to Dogbolter. There, Dogbolter orders Elgar to keep Alicia under guard, and offers Frobisher a drink and a chance to reconsider his position. Frobisher agrees to tell him everything if Dogbolter tells him exactly what the something is, but Dogbolter admits that he doesn’t actually know. Every other planet in Dogbolter’s empire thrives by manufacturing mediocre consumer goods, except for this world, which is delicately poised at an economic level which enables Dogbolter to make much more of a profit by ensuring that nothing is ever manufactured here at all. Dogbolter’s employees come in to work, fill out timesheets, punch a few useless buttons, stare at blank computer screens all day, and then go home. But now Arthur Gringrax, an unimportant low-grade button-pusher, has placed Dogbolter’s profits in jeopardy by actually creating... something. Nobody knows what that something is, but it’s new, something which could inspire other people to start making somethings of their own, until the planet is swarming with new and interesting ideas.
Frobisher admits that he has no idea what or where the something is, and Dogbolter, furious, calls in Elgar and shoots him dead just to make a point. He’s willing to tear every single person in this building to pieces just to get the something, starting with Alicia Mulholland. Frobisher realizes that Dogbolter isn’t bluffing -- and he realizes that, for all he’s said to the Doctor, he’s no hero. He thus admits that the something must be in his office; when he caught Alicia he assumed that she was searching his office, but she must have been hiding the something there.
Dogbolter sends a thug to search Frobisher’s office, and has Alicia brought to his own. The thug eventually returns with a small, innocuous box. Despite himself, Dogbolter is curious -- and he simply doesn’t have the imagination to figure out what the something might be. Alicia refuses to tell him, and, frustrated, Dogbolter orders Frobisher to open the box and see what the something is. Inside the box, Frobisher finds a computer chip, and after struggling with temptation, Dogbolter gives in, plugs the chip into his computer and waits to see what happens. A text message appears on his screen: “You don’t have to be crazy to work here, but it helps.” To Dogbolter’s horror, Alicia reveals that this message has now been beamed to every computer in the building. Even in his private office he can hear the laughter, as the workers read the joke, get it, and cheer up just ever so slightly. Now they’ve started thinking, and soon they will start talking to each other, sharing ideas, and making somethings. The economy has collapsed, thanks to Dogbolter’s curiosity.
Enraged, Dogbolter pulls a gun on Frobisher and Alicia -- but the TARDIS materializes in the path of the bullets. The Doctor pops out of the TARDIS to ask Frobisher one last time if he’s reconsidered, but Frobisher sends him back into the TARDIS to wait while he confronts Alicia. Dogbolter has fled, but Frobisher won’t let Alicia go after him until she admits that she was using him and tells him what happened to Arthur Gringrax. She reveals that there never was an Arthur Gringrax -- and transforms into a penguin herself. She is Frobisher’s ex-partner and ex-wife, Francine, the Whifferdill he loved so much that he stayed in the shape of a penguin for years to remind himself of her. She was “Arthur Gringrax”, and she was also the bloodstain in the hotel. She needed Frobisher to lure Dogbolter into her trap, because she knew that Dogbolter would only trust a man truly without guile... and because she knew that Frobisher was honourable enough to stick with the case to the end. He was always a better person than the cynical private eye he pretended to be, and perhaps that’s why they had to go their separate ways in the end. Frobisher transforms back into the shape of a penguin as they kiss one last time; she has her own battles to fight here, and she knows that if Frobisher doesn’t get in the TARDIS, he’ll regret it -- maybe not today, maybe not (et cetera). Frobisher and Francine part once more; Francine to resume her struggle to bring Dogbolter to justice, and Frobisher to travel the Universe with his friend, the Doctor.