While we are entranced with "fearless leader" fascism and people like Mussolini, or Hitler, an examination of fascism around the world finds that visionary leaders like them are rare, and most Fascist movements have not been the genius of a single person, even when a single person gets credit for them. Franco was the general who prosecuted the coup and civil war that established Fascism in Spain, but he wasn't even its ideological founder. Pinochet was simply first among a cabal. The leader of Portugal's fascism movement was selected as an economist who promised to fix Portugal's economy. Fascism loves it's fearless leaders and tries to find them, but if they don't perform as expected they do get dumped. The politicians and military strategists are really like Dogs on a leash. Juan Peron was dumped by his own founders when he crossed path with the wealthy and Catholic Church. Mussolini was dumped by his own followers, put back in power by Hitler, and eventually hung upside down from a Fence. Fascism is not kind to fearless leaders who don't live up to those holding their leash. When Juan Peron's second wife tried to continue ruling Argentina after coming to power from his enthusiastic backers -- when those backers saw she was not following orders they staged a coup.
Argentina's reign of terror was managed by three drunken military leaders from the Navy, Army and Air Force. They militarized the police, tried to capture and kill anyone who was a socialist. And since they were using Ayn Rand's definition of socialism as equal democracy, and Hayeks premise that any socialism (including social democracy) inevitably leads to left wing fascism, they went to war with most of the urban population. They sent teams of soldiers around the country in Ford Falcons snatching people, torturing and secretly trying them, and then dumping their bodies in the Ocean (or other still not found places), and all on the motto "you must have been guilty of something."
Fascism is usually about defeating socialism and reestablishing order, so it is often as "bottom up" in it's implementation as any other movement. Just the bottom is usually the land-lords, business leaders, and military officers. It's also advertized based on nationalism. So it's entirely possible for fascist states to go to war with each other. When Hitler started his "unification" program targeting his home state of Austria, the Austrians resisted. They had a dictator named Dolfuss who was an admirer of Mussolini, not Hitler. The little guy was trying to get control of Austria by imposing martial law on workers, killing Union leaders, and breaking Unions. His economic advisor was Von Mises and the two were close enough so that when Dolfuss sent his wife to refuge with Mussolini, Von Mises sought a chair in Switzerland. Dolfuss tangled with the Nazis and they sent an assassination team to kill him. But before that they threatened Austria and Mussolini backed his little friend Dolfuss. Mussolini threatened to go to war with Hitler. A lot of folks would have liked this. But Mussolini met with Hitler and liked that little guy better than the other little guy. He withdrew support for Dolfuss, looked the other way, and Dolfuss was assassinated by a team of Nazis in broad daylight. Von Mises went to Switzerland and then on to the US; and pretended to be anti-Fascist the rest of his career. Fascists can and do go to war with each other.
Argentina was like an enthusiastic dog during the Reagan program to repress socialism in the Americas. They sent teachers to El Salvador to teach the Salvadoreans (as if they needed teaching) how to "collect intelligence" through torture more efficiently. They were backed by Reagan and Thatcher in the whole operation Condor and anti-"Communism" effort. The Vatican backed them, while pretending to be pissed that they were killing over-enthusiastic monks and nuns. The Vatican had it's war on Vatican II and "liberation theology" and it made a grand alliance between nominally warring parties.
But then the Argentines attacked the Falklands. Fascists can go to war with each other, and this is because they always are serving oligarchs. Fascism has always been elitist, and if the fascist parties elevate leaders to be "new oligarchs" they do so serving the old oligarchs or the "old oligarchs" yank their leash.