How to Preserve the First Spanish Republic?

During the Third Carlist War, the First Spanish Republic was formed when King Amadeo I of Spain abdicated and there was no clear successor until the eventual restoration of King Alfonso XII to the throne. However, the Third Carlist War was the final conflict in which the Carlist faction under the claimant-King Carlos VII had a chance to seize the throne from his relative. Yet, the First Spanish Republic was doomed from its inception, as there were massive divisions within the Republican movement, and it only took one Arsenio Martinez Campos to launch a coup against the First Spanish Republic that precisely led to the Bourbon Restoration that allowed Alfonso XII to become king (his son would preside over Spain's loss of Cuba, Puerto Rico, and the Spanish East Indies).

Was there any possible solution to fix the problems that plagued the First Spanish Republic? In addition to the Third Carlist War, there was also the Ten Years' War, or rather the First Cuban War of Independence in which Cuban separatists revolted against Spanish rule, and the subsequent Virginius Affair that almost led to war between the US and Spain in the same time period as the Ten Years' War and Third Carlist War. One other possible effects of a surviving First Spanish Republic would be its possible policies towards its colonies. At that time as well, the Philippines was under the infamous Rafael Izquierdo y Gutierrez, known for the execution of three Filipino priests that would be known as the GomBurZa trio after the Cavite Mutiny was suppressed.