I'm sorry to hear that your fellow Arthur ingested an unknown quantity of vitamins, but pleased to hear that he seems relatively fine so far.
Since it has been over 2 hours it is really too late to induce vomiting and try to remove them from his system before he absorbs them. They are likely out of his stomach and into his intestines by now.
Most one time vitamin ingestions are fairly harmless. Repeated overdoses are where we tend to see trouble.
The exception would be large quantities of vitamin D. A big overdose of vitamin D can cause tissue and organ calcification and kidney failure.
But if these were a mix of multivitamins then it is unlikely he will have any long term effects from this.
He may have some nausea and loose stools for the next 24-48 hours, but that should be it.
To try and settle his stomach if he seems a bit nauseous you can give either:
1) Pepcid-ac (famotidine) at a dose of one half of a 10mg tablet per 10 to 20 pounds of body weight every 12 hours.
2) Prilosec (omeprazole) at a dose of one quarter of a 20mg tablet per 10 to 20 pounds of body weight every 24 hours.
These will reduce stomach acid and should help with nausea related to simple gastrointestinal irritation. They can be given for several days if need be.
Then start a bland diet of 1/3 boiled, lean hamburger (or boiled, white, skinless chicken), all fats and juices drained off the meat, mixed with 2/3 boiled, plain white rice. Feed several small meals a day. You might wish to add 1 tablespoon of canned pumpkin to each meal if you are seeing mucous in his stool as fiber helps soothe an irritated colon.
You can also add probiotics to his bland diet to replace the good bacteria lost with intestinal upset and diarrhea. Good brand name products include Fortiflora, Proviable, or Benebac. They can be found online or at pet stores.
Once he feels better start mixing in his regular dog food very slowly, less bland more regular with each day. It should take a week or so to convert him back.
If he is vomiting and begins feeling poorly though it would be best that he see a veterinarian as anything you give orally will just come back up worsening his dehydration.
But if he continues to remain fine and this was not a huge dose of vitamin D you may not need to do anything.
Please let me know if you have any further questions