Also, the character setups from the Trek shows are designed for long running TV shows. They have a Klingon there for the potential of future stories, for example, and they didn't use him for quite a while. The whole setup Captain, First Officer, Navigation, Ops, Tactical, Chief Engineer, Counselor is based on that.
If you don't want to write a season full of stories, I think you should be asking yourself "Why do I want a half Vulcan/half Klingon in here?" What is the purpose of that character in the story? Basically, ask that for all your characters and you should come up with something that doesn't feel like it's been copied from a blueprint. If you want a crew full of aliens and hybrids, what are you going to do with them?