There’s no special attribute in the Solution articles that can help with different visibility configurations. But, the articles can be added to different folders that can be attached to specific portals and hidden in the other portals if portal-level segregation is fine.
If require granular control over visibility within a portal, the portal customization is the way to do it. Solutions Home section in the portal pages can be customized. But, I do not have any examples for it and am not sure if your requirement might be completely possible with it. Consider it as a workaround.