Hello, my name is***** and I have over 20 years of experience as a veterinarian.
I am so sorry to hear that Zeus is licking his feet excessively, has nails that split easily and now has darkening around the base of the nails. This is definitely abnormal.
Does he lick and chew anywhere else? Certainly dogs with allergies, especially food allergies, will often lick their feet, but they will often lick or scratch other places too.
If he had a single affected nail I would be suspicious of some sort of trauma or even a tumor of the cells that make up the nailbed.
But because this is affecting multiple nails there are several other things that may be causing this. Bacterial or fungal infections as well as vasculitis (blood vessel inflammation) and autoimmune diseases (immune system attacking the animal's own body) like lupus or pemphigus as well as endocrine diseases like hypothyroidism are all possible causes of nail abnormalities.
Has he had some screening blood tests done? I would include a complete blood count, biochemistry profile and thyroid profile, making sure they check a full thyroid profile, not just a T-4 alone as that won't be helpful.
If those look fine then bacterial and fungal cultures of the debris present at the base of the nail should be done. If that is not diagnostic then a biopsies of one of the affected nailbeds and his skin around the nail may give you an answer.
Treatment recommendations will be difficult until we know why his nails are affected.
It is worthwhile to start omega 3 fatty acids however as they are natural anti-inflammatories and are important in maintaining skin health. I recommend an omega 3 fatty acid dose based upon the EPA portion (eicosapentanoic acid) of the supplement as if we do that the rest of the supplement will be properly balanced. Give him 40mg of EPA per kilogram of body weight per day or 20mg per pound of body weight per day. For example a 50 pound dog could take 1000mgs of EPA per day.
Since an antihistamine was helpful in the past you might try Zyrtec (Cetirizine hydrochloride) at a dose of 1/2 mg per pound of body weight orally every 24 hours. That would be one 10mg tablet per 20 pounds of body weight. (Make sure it is NOT the formulation with a decongestant (such as Zyrtec-D) because cats and dogs cannot tolerate decongestants.)
Food allergy is very possible with him as the feet tend to be more reactive with food allergies, especially if his feet seem to be itchy all year round. Dogs can develop allergies to any protein or carbohydrate so even if he is only fed one thing that can be what he is allergic to. Dogs with food allergies tend to lick and scratch their paws, face and ears the most, but any of the "allergy reactive areas" can be affected.
Make sure that the food that you put him on is a true hypoallergenic diet. The trouble with "limited ingredient" or "low allergy" pet store brands is that the same machinery is used on multiple lots of food without sterilization cleaning in between. So for example even if a food says it has salmon and rice if the previous batch had beef and corn then you will get traces of those ingredients in your bag of food. Not a big deal if your dog isn't allergic but a waste of money thinking that the food was hypoallergenic and not good for your dog if those happen to be allergens for your dog. The veterinary brand true hypoallergenic foods are more expensive because it isn't cheap to thoroughly remove all traces of a previous food mixture from the machines used to process food.
Generally what I recommend is trying to clear the skin and then adding one food item (chicken, beef, corn wheat etc) every month to see what they react to. Then we can find a regular food to try. As far as permanent diets I do tend to stick with Purina Pro Plan brands or Nature's Recipe as I find those rarely if ever have cross contamination. Purina Pro Plan Turkey and Barley or Nature's Recipe Vegetarian or Venison are pretty good products. I know that this isn't easy from personal experience (my dog is allergic to wheat) and it is time consuming, but worth it.
If you choose to try testing/treating him for a food allergy I recommend that you try a true hypoallergenic diet like Hills z/d or Purina Veterinary Diets HA. No treats, flavored medication or bones while on the diet and it must be used for a least 12 to 16 weeks to see the full effects. You should see some improvement in 6 to 8 weeks.
Here is a link to an article discussing nailbed disorders which you and your veterinarian may find helpful: http://www.ivis.org/proceedings/navc/2005/SAE/110.pdf?LA=1
Let me know if you have any further questions.