I wrote a whole fic about this called Bloodstuck, and it mostly centers around the Blood aspect. I think some of the powers a Blood player would have would vary but would always have to do with the idea of "connection" and relationships with other people. A Blood player would be able to help mend the rougher patches in a parties relationships, either by holding everyone together long enough to complete a goal, or seeing what relationships wouldn't be beneficial in the long run. Depending on the Class you get, I think you'd interact with these relationships in your party quite differently.

So in Bloodstuck, Karkat is a Knight of Blood which allows for him to strengthen people's relationships and bonds. He is able to bring people together by protecting their relationships, making people see the right path or make the right decision when it comes to this. Because people are around him, it makes them want to better their relationships with one another.

A Seer of Blood would be able to literally see the rough patches and good patches of any relationship, and what needs to be done to make them break or fix them. I think this would take the form of being able to see a persons past actions towards another, or maybe being able to see what someone else will do in the future. Another interpretation is that they might be able to see if a person will go well with their party or not, like literally they'd be the only ones who could accurately judge a book by it's cover lol.

A Witch of Blood would probably be able to forcefully make people come together by manipulating the relationships, like making people like one another for a short amount of time or making everyone hate each other. Because Witches tend to take on a more literal role for their Aspect, I also think they'd be one of the few Classes who could actually do something with Blood like maybe they could Blood bend avatar style or something.

These are just some of the ideas about the Blood aspect I've thought about for a while lol.