As I was going through this thread the first series I thought of was Frederik Pohl's Heechee books -- curtw beat me to it.
Another book I thought of that kind of matches your specs is Earthblood, by Keith Laumer and Rosel George Brown. The (nearly) extinct race is humanity. There are many alien species, but a full human (100% Earthblood) specimen is a rarity. It is very much "old school science fiction," which you'd expect from Keith Laumer. Until recently it was available from Baen -- right now it's marked "unavailable." You might want to keep an eye out for it, or pick up a used paper copy.
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