+1 to what
@jbutler said. You can't force fun into the structure... and any attempt to change the "usual" game is very liable to backfire and make people unhappy.
I've put 11 at my 10-player holdem' table. I have ten chairs and a stool... last player gets the "stool sample."
If it's literally too tight (some of my regs are, um, wide), I'll get up when the 11th (or 12th) player arrives and sit out. Honestly, I've never missed a night when hosting, so I've played more hands than any of my regs. I'm usually busy doing hosting stuff, buyins and rebuys, pulling shots of coffee, etc. Also, my dogs like to take a quick relief run, and it's nice knowing that the table can run itself while I go outside. (I have good regs; your mileage may vary.)
One thing that does help, in a packed house - aside from having a computer with a web browser hooked up to the TV so that the odd person out can find funny shit - is to give players waiting for a seat dibs over re-buys for bust-outs. Most of my regs see this with a sense of fairness, and want everyone to get to play... and so they actually loosen up and are more likely to go all-in. This means more bust-outs and rotation in and out of the game, and generally more fun on the night. Personally, I became less likely to top-up after a big hit... instead, I'll try to double up or bust out, and take a rotation through the "out" position.