Regarding issuing uniforms to a specific company, the answer is yes. You have to understand how the depot system worked.
For a quick and dirty, the QM department let out contracts for clothing and these were, when completed, sent to the nearest depot. They were stockpiled and issued as requests came in. However, that didn't mean that a depot only issued to troops in it's geographical area. If one depot was short a certain number of, say, jackets, it was send a request to the next depot, or to whichever depot had sufficient numbers on hand to make up the balance of the order.
As regarding specialty uniforms, such a zouaves, Berdan's, or anything NOT on the regulation clothing list, a unit commander could request the issuance of such clothing to his command. However, there are a couple of caveats in play. A fully sewn/constructed uniform, to include cap, trousers, vest (if needed), leggings, etc, was to be forwarded to the depot, along with a list of the numbers required, and how many of each size. The depot would then contract to have them made, or perhaps made them in house. It all depended on work already being done, manpower to hand, etc. In addition, the cost of the clothing, minus the government allowance for regulation clothing, was charged to the Colonel of the regiment (or captain of the company)and he had to fully pay that bill before the clothing would be forwarded.
This system was the same for both sides during the war. For example, there exists in the Mannassas NPSmuseum, a jacket, which is a part of a uniform made under contract for the Washington Artillery in Lee's Army. These were paid for by the unit itself, and produced at the Richmond Depot. The jacket is made of English Army Cloth and piped in red worsted wool on collar, cuffs, and the front edge. The cap and trousers were likewise made of the same material, and with red piping where appropriate.
So yes, it is fully possible that one company from the 76th could have had zouave clothing made and issued to them, at whatever additional cost it might have been above the normal soldier's allowance, provided that the Colonel approved of the contract.