There seems little likelihood of immediately finding advanced space aliens, so searching for a companion species has to be turned back to the species we have here.

Aside from advancing the intelligence of dogs, which I think should be done, we should also consider some other primates. They wouldn't have as far to go as canids and have a structure we know is suitable for larger brains.

I would consider some monkeys, but first the apes should be candidates. Not chimps, though. Chimps are trash primates, always squabbling and fighting, cheating their own relatives, even, and have seemingly unpredictable emotional states.

Instead, I think orangs would be better. They are slow and deliberate, usually good natured, able to live independently on their own or to form larger groups and so are socially versatile -- neither dependent on company nor incapable of organizing. They appear to have a good deal of mechanical ability, and while they can be dangerous or even murderous, they appear less so inclined than our closer, trashy relatives.

Further, they are somewhat more removed from us genetically, and so may prove more interesting as a companion species.

For the next superintelligent species I'd recommend orangs even if we can one day clone a neandertal or two.