The European Union is constituted by 28 member states, and not all of them are republics. For example, Spain, Belgium and the Netherlands are constitutional monarchies.
It is not a partnership but a form of supranational integration. The level of integration is not as deep as the one that can be found in a federal country like the US. Its member states have established a common market, free movement of people and goods, a common currency, common foreign policy and even certain levels of political integration. Many other aspects such as the fiscal policy, are decided at the state level and the EU has no authority over them.
