In Italy the fascist movement managed to attract adherents from all strata of society.

To the little bourgeoisie, the countryside folk, and big industrialists alike the appeal of order and social harmony to prevent a violent communist revolution was strong.

A part of the conservative elite also, like it happened to Hitler, they handed over power to Mussolini in the hope of them controlling him.

The Monarchy and much of the army also, because of fascist myth of the Italian “mutilated victory” (ie. the liberal politicians betraying the fighting soldiers who gave their lives by agreeing unfavorable peace terms).

There was also a large part of the cultural elite that adhered to fascism, D’Annunzio, at the time the most famous writer in Italy, and many that created the Futurist movement. They were attracted by a non-communist revolutionary movement.

As fascist in its early form was not antisemitic (though of course many fascists were), contrary to nazism, even many Italian Jews, especially among war veterans adhered. One of Mussolini early biographer and lover was Margherita Sarfatti, herself a Jew. All this changed of course after 1938 and the proclamation of racial laws.

Anyway, back to your question. Yes, Fascism in Italy was a large popular movement that attracted sectors of the elites. And this attraction wouldn’t change before Racial Laws and the entry into war alongside Germany in 1940.

By early 1942 with the disasters of the African and Russian campaigns the regime was already unpopular and Mussolini especially. In 1943 the first workers strikes took place, the Catholic and Communist resistance started to organize properly. By then, the regime itself to try to save fascists institutions deposed Mussolini. And this is another testament of fascination of the elites towards fascism, as they deposed the dictator not the dictatorship.