Would a transnational armed force be capable of forming

Question

In my current world, the main political faction, called the United Commonwealth and made up of multiple independent nations acting together,has established both the United Commonwealth Army and the UC Navy. These two are made up by personnel recruited from acoss the member states of the UC, and work, train and are led collectively.

Now, without going into problems about implementation and organisation, would it really be possible to create such an international force? If not, how could I make it possible?

Context

• The countries are all democratic and free market based
• They broadly agree on most foreign policies
• They share mostly common enemies
• They are not all equal in terms of size, population, economy, etc.

Edit: I apologise if the original question seemed inapporpriate. If I was unclear, what I meant would be more akin to a theoretical EU army/navy, in the sense that soldiers would be under the organisation of a transnational body, such as AlexP's Eurocorp example. The point of the question was to ask what possible challenges would be faced by such an entity, and how would they be overcome.

Answer 1

Some people are already trying to make that happen

The European Union and NATO are examples of military alliances where different armies work together as one. As you point out, each unit still serves under its own flag. There are efforts to create a unified system in Europe akin to what you're proposing. Here's an excerpt from CAP (highlighting mine).

A major shift is needed because the current problems plaguing European defense are structural. The problem with European defense is less about spending and more about fragmentation... Integrating European forces, acquiring key capabilities, rationalizing and harmonizing the sprawling EU defense sector, and investing in cutting-edge research are some of the areas where the EU could play a critical role.

This is a controversial opinion. Countries don't like giving up any level of control over their militaries for obvious reasons. But if your story has a big enough reason (especially an urgent threat) then I can definitely imagine a truly integrated military force.

Answer 2

Organizational Continuity
You cannot simply assemble a bunch of people and expect them to be a functioning army (or navy). Even if each is individually quite competent, they have to train with a common doctrine for years and years to become a professional fighting force.

Can your alliance provide that sense of purpose?

Funding
This continuity, and equipment purchases, must be funded for decades. You don't get a tank or a fighter aircraft by mail order. Contracts are negotiated which are the basis for building the factories. A democratic central government has enough problems to provide that money for decades at a time.

Can your alliance provide that fiscal discipline?

Motivation
What makes people risk their life in battle? Flag and country play a big role.

Can your alliance provide that rallying cry?

Maybe. Or not. You can write your story either way.

Answer 3

It's possible, we have NATO/Warsaw Pact as recent guides, as well as UN Forces (though they're not as analogous IMO) Looking back in time, you might also find Revolutionary-Civil War America (especially the CSA) and the Austro-Hungarian Imperial&Royal Army as an interesting microcosm of the idea. Interestingly the biggest problems these forces have tend to be political. For example:

What language do we speak? Armies fight best when everyone speaks the same language at least well enough to receive orders. Realistically on a modern battlefield you need to speak the "Army" language fairly fluently, to be able to rapidly get across complex ideas. That argument alone could last years and lead to terrible politically-expedient "solutions." For example, the A&H military in 1914 had units that spoke their native language, led by officers who spoke it fluently as a second language. But the moment these units started taking losses the replacement officers often didn't speak their regiment's language! Or regiments would have maybe one person in several hundred actually capable of speaking German/Hungarian well enough to receive orders from higher up!)

What equipment do we use? The member-nations will have competing industrial concerns. Producing for the combined military might of the alliance is a HUGE financial boon to whatever nation can secure a contract. Take the eternal EU-arguments over having a EU Military. Do they use German tanks? French ones? British? (pre-brexit) Maybe a whole new design incorporating tech from each country? And it's not just tanks, rifles, radios, rations, you name it! It's exceedingly unlikely they'll just "take whatever is best" because "best" is somewhat subjective. But more to the point, they don't want to give any one nation too big a sway over the military. If Bregoland provides all the tanks, aircraft, trucks, radios, and rifles for the alliance, Bregoland can nix potential military activity by going "hey we're not going to produce these goods anymore." So Bregoland, Utopistan, and everyone else each produce one core piece of military hardware. Except Bregoland really DID make the best of all the things I listed before, so you go to war with second-rate Utopistan tanks/whatever. Or maybe Bregoland gets overrun in the first six weeks of fighting, and suddenly you have 0 tank manufacturing capability because literally all of it was in Bregoland because politics. You foresaw that possibility, but for economic reasons you couldn't ding Bregoland's already-smaller-than-Utopistan's GDP by allowing production elsewhere.

Where we Fighing? You say they have "mostly" common enemies. That's a Big Deal. If Bregoland and Utopistan are sworn enemies of Country X but only Bregoland hates country Y... what happens? You might find Utopistan forces behaving like CSA states in the American Civil War, where some states forbade the use of their forces outside of their state/the CSA. You need firm laws and the political will to follow them. If each nation-state specializes what then? If Utopistan provides your alliance's aerial reconnaissance squadrons, what happens if they're deployed "for defensive use only?"

All these are difficulties that can and have been overcome. But they're just as likely to overly-complicate your military and can result in critical failures that cost the alliance a war.

Answer 4

UN stabilisation missions are composed of members of different militaries acting together in exactly the way you describe.

Note the UN blue helmet and the national flag on the arm.