Trying to type a close friend of mine. . .
She is a lot like me, but I've noticed that she tends to be very concerned about making sure i'm physically comfortable, and comes off as sort of a caregiver. She also seems to use Fe a lot (a bit more than I think i do, but I guess i'm not always aware of using it), but that could be demonstrative Fe I suppose. She is also a great listener, better than me I think (even though I like to think of myself as a good listener too when people come to me with problems). She also has a very sharp sense of style and puts together very elegant outfits in no time, and mixes together various perfume scents that complement each other amazingly well (I am very weak with respect to these abilities). She is also very hospitable to any guests (not just me), knows how to welcome them, make them feel at home, etc.
In terms of how she is like me, both of us care a lot about each others' problems and spend time together confiding in one another on a one-on-one basis. We are both pretty good at empathizing and understanding what is going on psychologically, and giving advice the other finds very comforting and helpful.
So, the two possible typings i've come up with are SEI and IEE. In many ways she is so similar to me it seems like we're identicals. But in other ways, she seems to have good ability with Si, but she is definitely a feeling type (uses a lot of Fi/Fe), so not SLI or LSE or EII. Doesn't seem like Se is a big component of her behavior, so I dont think SEE. Maybe our close relationship and good understanding of each other is because we're semi-duals, hence SEI?