All birds are unique, but I have a rescued White Capped Pi and I can say that she's very independent. She's also very hands-off, so she doesn't sit on us or like to be handled other than to be transported from known-place to known-place (such as sleep cage to big cage, or sleep cage to weigh scale to big cage, and sometimes to look out the window, but then she wants to go back to her big cage pretty quickly). She likes head scritches, but as another person said, on HER terms. We only have her, so I can't say how she would do with other birds (at boarding facilities, she ignores them), but we wouldn't be surprised if she got possessive, because she puffs up around people when I'm around (when I'm out of the room, she could care less about other people). If you can find a rescue in your area that has a Pi, or any bird, really, they would know more about the personality of the bird, since any baby bird's personality will be a crap shoot. I knew that our Pi was like this before we got her, but we were fine with that. She's perfect for us.
She's very food motivated so she has a decent level of training, which is great for a hands-off bird (I can tell her "inside" and she'll go into her cage on her own). She also communicates well when she wants to be left alone, which is great for not getting bit. Ours wants attention in the morning and the afternoon/evening, but during the day she's either napping, playing on her own, or simply staring out the window. She likes to be near us and with us, just not on us or touched excessively by us. She's much more into head scritches when she's molting, but that's for grooming pin feathers and general itchiness.
I've also had a Meyer's, which is another Poicephalus like the Senegal, and he was way more into being on me than my Pi. My Meyer's was also pretty independent, but he was also my little buddy and would ride me around the house while I did just about everything. My Pi would rather be near or in her cages, but have me where she can see me. Again, check with your local rescues to see if they might have a fit for you and your Senegal, even if it isn't a Pi. I've read stories about people who bought birds who ended up not getting along and it's kinda sad, because they live so long and are so hard to rehome if it doesn't work out. Good luck!
(oh, I'll also say that my White Capped is very pushy and demanding, which is supposedly common. We think she's awesome this way, and she has us wrapped around her little claws, but not everyone will feel the same.)