Without a doubt, the European Union should harmonize its tax systems to blanket member countries. Each country should pay similar taxes or at least follow the same taxation rules. Perhaps smaller countries with smaller economies could receive breaks and reductions. However, a uniform tax code would make the most sense.
Yes, the EU should further harmonize tax systems between member countries because it would be advantageous to have the same regulations. Each member would regulate accounting, accounts payable, and accounts receivable and they would be the same things. Additionally, having a similar vocabulary and a shared definition of accountancy, it will be easier to work with one another.