Aleve (active ingredient Naproxen) is not used in dogs because it has so many bad side effects and we have much safer nonsteroidals to use.
The only dose I could find was in Plumb's Veterinary Drug Handbook and that publication recommended strongly against its use. The listed dose is 1mg per pound. If he is 32 pounds and ingested the usual 220mg tablet size, that is 7 to 8 times a "normal" dose (32mg in Cooper's case). He very likely ingested a toxic dose.
The effects of this drug are first on his gastrointestinal tract, vomiting, diarrhea, ulcers (which can be perforating leading to peritonitis) as well as possibly on his kidneys (kidney failure) and liver enzyme elevation due to its toxic effects on the liver and in rare cases neurologic effects (incoordination).
Given how toxic this drug is ideally he would see a veterinarian now. Peak blood levels are within 3 hours of ingestion so it is too late now to induce vomiting, this drug is quickly absorbed. If it has been more than 2 hours it's too late to induce vomiting but activated charcoal may be helpful if it was given within the last 6 hours.
They can place him on drugs to help prevent and treat ulcer formation such as sucralfate, as well as intravenous fluid therapy to support his liver and kidneys. Unfortunately this drug hangs around a long time in a dog's body. The half life, which is the time it takes for half of the drug to be metabolized out, is 74 hours (3 days). So he may need treatment for several days. And I would expect you not to see the full effects for several days. If he were my pup I'd have him seen by a veterinarian tonight as the sooner supportive care is started the better he will do in the long run.
If you have no access to emergency care tonight then at home now you can start either:
1) Pepcid-ac (famotidine) at a dose of one 10mg tablet per 20 to 40 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one half of a 20mg tablet per 20 to 40 pounds of body weight every 24 hours.
Either one should be given for at least 10-14 days.
Then I would have him seen by his veterinarian tomorrow morning to start supportive care to try to save his kidneys and liver function and protect against ulcers.
I would not consider him out of the woods for 5-7 days.
I am relieved it has been a while since any ibuprofen, because that would make things worse, but he can still get sick.
Best of luck with your fellow, let me know if you have any further questions.
Please let me know if you have any further questions.