The only other country to send out as many people as England did was Portugal, which has kept exporting its own population even to the present day. While the demographic profile of these migrants was largely single men, degredado criminals, "King's Orphans" for marriage in Asia and of course the crypto-Jews, if they had a colony suitable for family settlement I don't see a reason why Azoreans, Madeirans (and mainlanders, just less than the islanders) wouldn't be interested.
In that vein, the Portuguese could've settled in North America, the Southern Cone, and the Cape of Good Hope areas. The latter two fit their agricultural toolkit at the time of colonization, and play into Aleixo Garcia/the Inca/Brasil and the Asiatic trade routes respectively. They could've have also settled Australia, although I imagine other locations would be more tempting. Of course, any of these colonies would receive competition from Brazil, but life in Portuguese Africa and Asia could be pretty tough (threadbare garrisons, tropical disease, etc.)
As for the other colonial nations, the key would be sending out more people to the right places. France feared having a Huguenot-dominated colony, and had relatively more land in Europe to settle internally. The Dutch IOTL achieved religious pluralism and a great deal of mercantile wealth, reducing the incentive to settle (so much so that even New Amsterdam was ~40% English. Not to mention the big Huguenot presence at the Cape.) The Spanish conquered the big ticket items early and at that point how do settler colonies, which require a lot of investment to bear economic fruit, compete with the New World equivalent of Powerball?
If you set up the factors, you could plausibly allow any nation within range to colonize the settler-friendly parts of the Americas. The Scandies are a good, plausible option; if a large German polity arises in Hannover a couple centuries early then they have location, maritime infrastructure and more than enough reason to get out of Germany. An alternate Castille, one which relies on the knowledge of Basque fishermen and gets boxed out of the rest of the Atlantic by the Portuguese, could also have easily colonized North America.
France is the other big what-if, but you'd need clear royal investment and not being neighbors to the British colonies for a slow-burn French colonization of Quebec (or elsewhere, if they can steal one of the various Brasilian ports they were interested in). In that vein, an Equinoctial France in a world sans the de Sa family, starting from alt-Rio de Janeiro, could definitely expand into the Southern Cone. The Jesuits weren't fully entrenched in Paraguay, Spain sent the Peruvian trade via Panama and hadn't yet created the Viceroyalty of Rio de la Plata, and extractive industries could be supported by the French equivalent of the bandeirantes in the interior.
As with Quebec, France would probably need to send more people, but they wouldn't be next to the massive demographic disparity of the British in America. Plus, they'd probably be the ones to discover the riches of Minas Gerais, and nothing brings settlers like a gold rush. The later option for them is of course Australia, but I think there'd only be the incentive to settle there if Colbert pulled off creating a French East India company (maybe they take the Philippines in an alt-WoSS?)
