I'm not a huge Ginny fan, well...any Weasley to be honest. I can't imagine Harry with his mother either. (Which is one reason why I really do not like him with Ginny--far too much like his mother.)
There are lots of threesomes that I read that are really fun and seem to balance well. If you are only talking about Severus and Harry; I read them with Lucius, or Draco, or Hermione, and I've read Luna as well.
My favorite two threesomes to read are HP/SS/DM and HG/SS/LM. Hermione plays well off of Severus and Lucius, and Draco and Harry play well off each other with Severus.
So, yeah, if you like to read them, they are out there. If they aren't your thing then...there is a lot of other stuff to read! Fandom is a great place.