Depends on what you define as global.
Having stuff like the Trent affair or the other various small incidents that happened between the UK and US during the ACW could expand it, and France would likely be willing to join against the USA as long as the UK does they have interests in setting up a Mexican Empire which massively benefits from a weakened US.
At that point the war is technically global as it covers five continents even if most of the fighting will be restricted to North America + Caribbean. From there you could make arguments towards Prussia, Austria and Russia (and to a lesser extent Spain). Prussia isn't a fan of France but also isn't friendly with Austria. Russia likes the US but doesn't like France or the UK, Austria doesn't like France, Prussia or Russia but is willing to work with France when the situation calls for it.
Too really expand it yous need at least two European powers joining the side of the US. Russia is most likely to join in opposition to France and the UK but are fairly limited as they can quite easily just blockaded at naval chokepoints, so they'd need another European major to give them a route to France.
Smaller powers like China and Japan could technically get involved but they'd be sideshows as they aren't the powers they'd be decades down the line.