A Qing loyalist named Zhang Xun tried to reinstate the Empire in 1917, but he wasn't trying to become the emperor, he was trying to restore the Qing with Puyi as emperor. And his attempt was arguably out of loyalty and habit rather than out of ambition.

AFAIK, there was no evidence of tangible plans for any of the other warlords to become a new emperor. It makes sense because Yuan was the most powerful warlord of that era, being the head of the entire Beiyang organization. After his death and the dissolution of his organization, none of the northern warlords could match his level of influence. After Yuan Shikai's and Zhang Xun's respective failed attempts, it was pretty clear that the ship had sailed that it was no longer viable to make China a monarchy.

However, plenty of warlords of that era did have the ambition. They couldn't try to become emperor, they tried to become president instead. Between Yuan's death in 1916 and the end of the Beiyang era in 1928, there had been 14 presidents in 12 years, and most of them were military men. You could argue that it was basically the same game, different title.