Queen + Knight is usually called an Amazon, but I have also seen Empress, Maharaja, or Terror. I'll try it if Oinquarki will set up a board for us.
Super Seirawan Chess

I'll use the Amazon for the queen+knight combination because I already have the piece drawn.
Players and pieces in hand:
White: ichabod801 A
Black: staggerlee A
Move list:
- e4 c6
- d4 d5
- Nc3/Hb1 Bg4/Hc8
- Be2 Nf6/Eg8
- e5 Bxe2
- Qxe2/E
I think you may find that the Amazon is just too strong relative to say the B, N or R.
I played S-chess once where the 2 extra (drop) pieces were the Champion and the Bear -- that was very good. You can read about the Champion at www.omegachess.com and the Bear is a jumper that can reach all 16 of the 2nd perimeter squares -- instead of just the 8 that the N can reach. The Bear is also called the Squirrel in some games. Personally, I like the term "Super Knight".
Both the Champion and Super Knight can fork like crazy!

What if we simply used the diagrams you can plug into chat, then when we drop in the new pieces, simply put in another bishop for the hawk, and mark in text that the bishop icon on square xx is actually Hawk, etc. You can go look at how Robert Brown and I are playing Seirawan Chess this way in the Seirawan Chess Group forums.
My idea for a variant. It is essentially Seirawan Chess, with a third new piece added, which moves as a queen plus knight. I can't decide how to name the new piece, I was thinking either "General" or "Heir" as in Heir to the King. The new piece is added just as the Hawk and Elephant are. Anyone want to play me a game? Beware I'll probably move pretty slowly.