As has been exposed many times in this thread, Spain can't control all of the Americas. It is too vast of a territory to settle, defend and even explore. It is also worth noting that not all lands in the Americas are equally valuable, why settling in New York and having to start from scratch when you can go to Mexico and simply buy a house in an already existing city with a functional agriculture? New settlements are very difficult to pull off succesfully, Roanoke is a very good example of how easily a colony can fail, Buenos Aires even failed once before its refounding. Colonists would prefer to move to areas where infrastructure already exists while merchants would prefer to settle in areas with established markets and large populations that could buy their products. This is part of the reason why the Spanish didn't push much further from the Aztec and Incan heartlands in the Americas, as they provided a headstart compared to new settlements.
However, new settlements can still occur if there's an incentive to them, the best incentive being the possibility of economic profit due to a natural resource that is located in the area. And of those there are plenty in North America. For starters, there are abundant gold mines in the Southern Appalachians, and the De Soto expedition allegedly encountered natives that worked with that gold, so the rumors could spread and the Spanish could attempt to establish a colony in the coast, preferibly at the mouth of a large river to move upwards towards the gold mines. The Spanish actually tried to settle in the Carolinas under Lucas Vázquez de Ayllón in the 1520's, but the settlement failed due to the loss of the supplies during a storm and a slave uprising. French Huguenots also tried to settle in the US southeast, both in Florida and the Carolinas, with both settlements thwarted by the Spanish. It's not difficult to think that the Spanish could have set up a chain of posts in the area to keep further French settlements at bay, thus eventually securing control of the Carolinas. But the Spanish went further than that IOTL, as they tried to colonise Virginia (Axacán) in 1570 employing catholic missions, but the colony failed. If you keep Axacán around, and have the Spanish discover the gold in the Southern Appalachians, everything south of the Chesapeake would eventually become a Spanish colony. The Spanish could try to push further north, as allegedly the natives in the Allegheny mountains told Pedro Menéndez de Avilés that he could find the Northwestern Passage by travelling across the mountains into the Ohio River, which obviously wouldn't work, but would give the Spanish a headstart in the Upper Mississippi basin. And speaking of the Mississippi, when De Soto interacted with the tribes in the lower parts of the river, the Mississippian culture was still somewhat intact, with relatively large settlements and working maize agriculture (which depletes the soil incredibly fast, that's part of the reason of their eventual collapse). If accounts of large quantities of Indians reach Spain and a religious company (say the Jesuits) takes interest in converting them, the Spanish would gain control of the lower Mississippi, albeit by 1550 it would be difficult to keep such a colony, as native populations would plummet due to disease rapidly, but Spanish imports of new crops could allow a higher population at a later date. If you combine this lower Mississippian colony with Spanish attempts at crossing the Appalachians from Virginia, you could have Spain control most, if not the entirety, of the Mississippi basin, reducing potential rivals to the Saint Lawrence / Great Lakes, and the northeastern coast of the US.
If the Spanish settle as north as Virginia, they would also encounter larger populations of American beavers (their range extends all the way to Mexico, but in smaller populations). This gives the Spanish access to the lucrative fur trade, which would further reinforce Spanish control of the Mississippi. Finally, the last potential colony the Spanish could get off North America is Newfoundland. It lies west of the Tordesillas Line, is visited regularly by Basque fishermen, and has abundant reserves of cod, a type of fish that was key to the contemporary diet. There's no reason why the Spanish couldn't settle in the island, the Portuguese tried a couple times after all. However, competition with the English and the French will be fierce in the coming decades, and with Newfoundland being an isolate colony, it could be taken by other powers eventually. Even with secure control of Newfoundland, I don't see the Spanish going further towards the Gulf of Saint Lawrence though, apart from trying to find the Northwest Passage, there's not much incentive to go there, especially when compared to the rest of the empire.
Finally, the Spanish could reinforce their presence along the extremes of the continent, especially in the Pacific Northwest and Patagonia. At the time, the Mapuche wars were in a phase of strong intensity, with the Spanish control of Chile being disputed. If the Spanish do better in these wars, they could expel the Mapuches to the eastern side of the Andes, thus granting Spain complete control of the Araucania all the way to the Chiloé island. In the 1570's the Spanish tried to settle in southern Patagonia and Tierra del Fuego, in order to secure control of the passage between the Atlantic and the Pacific and prevent future raids like that of Drake (we'll be back to him in a minute). The colony failed as the Spanish settlers did not expect the climate to be that cool and windy (it wasn't wise to bring Andalusians out of all people in Spain to the coldest part of South America), with the lack of resources causing the collapse of the settlement in the coming decades, to the point where English explorer Thomas Cavendish renamed the settlement "Port Famine". This doesn't mean the settlement is doomed, but it would have been hard to pull off, especially once a new route south of Tierra del Fuego begins to be used widely. Finally, we have the Pacific Northwest, the area was explored by the Spanish as early as the 16th century, and California was one of the places where Drake established temporary bases to attack the Spanish (New Albion). The Spanish could launch retaliatory expeditions towards California and create some settlements or garrisons, which could eventually extend all the way to Alaska. The Spanish tried to do this in the late 18th century, but by that point it was too late, and the British managed to push the Spanish out of British Columbia in the Nootka Conventions. If the Spanish settle in the area a century or so earlier and enter the fur trade in the PNW, it'd be very difficult to dislodge them. The Amazon basin could also be taken as an alternate route for silver and gold mined in the Andes to reach the ocean, albeit Portuguese bandeirantes would dispute it. Speaking of Portugal, a continued Iberian Union would grant Spain Brazil, and with it pretty much all of South America.
Alas, the Spanish don't have to do all the work themselves, once/if the American Empire breaks apart, the new states that emerge in the area can continue the colonisation progress, as shown by the Chilean and Argentinian conquest of Patagonia. If everything that I have mentioned was carried on, the Spanish would control close to 80% of the Americas, albeit most of it would be a nominal control, only holding it because nobody is willing to dispute Montana or the Patagonian wastes.