The US went to war with Mexico. Or, more accurately, Mexico went to war with itself, and the US supported the secession bloc well enough to legally adopt it.

Then the US went to war against its own secession immediately afterward.

Mexico, the United States, and the Confederate States are (were) all democratic republics, and their constituent states are all democratic republics.

And does it have to be a shooting war? Because democracies wage economic wars against each other quite frequently.