The idea Of the Spanish Empire forming a system of dominions in a similar manner to the British Empire has been discussed several times, but what would it take to bring it about? How can the development of responsible government in Canada be mirrored in Spain's American Empire? which of the colonies could be eligible for this system to develop?
There were several initiatives both partially implemented and stillborn that might have resulted in the foundation of a later commonwealth. There was one famous one that popped up a couple years ago, but has since disappeared that would have involved the Spanish King becoming Emperor in his own right, with the New World territory being divided into three kingdoms with their own constituent nobilities. The original source for this idea is lost to me, but I believe it was abandoned because of an unwilling monarch and a lack of close princes.
Later on, when Mexico became independent it sought a crown from Europe and had looked to a Spanish prince before the King forbade it. They shopped around for other potential monarchs, but that failed resulting in one of the leaders declaring himself Emperor. An action that had damaged some of the monarchy's legitimacy, and later his inability to mediate between emerging factions resulted in his deposition. The conservative element in Mexico continued to want a monarchy, and Napoleon III provided one in the form of Maximilian. However, the conservatives rapidly turned against him since Maximilian was almost as liberal as the liberals they were in a civil war with. Maximilian made a number of overtures for peace, offering to make the opposition leader his chief political official and adviser. When that did not work, Maximilian went to war but was not nearly ruthless enough in either persecuting the opposition, nor in sustaining strong conservative support. Conservatives were separated between those that wanted to get rid of monarchy all together in favor of a dictator like in other countries, those that wanted a different monarch and were courting for other possibilities, and those that remained loyal to Maximilian. Maximilian was able to gather the loyalty of many moderate conservatives, several of whom fought with him to the bitter end and a few of which died with him or fled into exile. The opposition, however, capitalized on growing anti-french sentiment and the idea that Maximilian was just a foreign conqueror without legitimacy. Following the conclusion of the American Civil War and with broad support from the US, the northern liberal rebel forces had all but one the conflict. The French, who were in this for their own self interest, left when the venture became impossible. Maximilian remained behind with those men and women who stayed loyal to him, and chose to die in Mexico even when defeat became certain. His last words before his death by firing squad were "I forgive everyone, and I ask everyone to forgive me. May my blood which is about to be shed, be for the good of the country. Viva Mexico, viva la independencia!"
But that's a bit of a digression. Overall, there were many who would have had a monarchy, particularly in South America south of Peru and in Mexico. Even the most republican areas around Colombia became republican by way of effect since they were opposed by the Spanish monarchy and looked towards an American Revolutionary example when it became clear that no foreign prince would come to claim their crown and Bolivar developed his own persona as a Napoleon like figure.