How can we boost the horsepower in our 2006 Cadillac CTS?

You can always get more power. Trouble is, it'll cost. You get more power by burning more fuel. If you had a dragster-slash-caddy, you'd get about two miles per gallon. The manufacturer put a small-displacement motor in the car so the owners would get good mileage, not neck-snapping performance.

If you try for more horsepower, you'll get a lot worse economy. Sure you want to go there? If you want performance at any price, you can do a few things, all of which burn more gas. First option- make the motor spin faster. You can get cams put in that will let more fuel flow through the motor (longer duration, perhaps more lift for the valves) but this won't be cheap. You might find an aftermarket turbocharger that would push more air (and fuel) through the motor. Not cheap to install, but might work if you drive moderately most of the time. Or you could get another, larger motor. More displacement means more fuel burned, which means more power.

You could also try for a nitrous injection system- your car would be the same, *except* for when you hit the nitrous switch, then you'll have a lot of power. Cost is less than other options, but it's something only for when you need a lot of power. The nitrous bottle lasts only a short time, too. ... Take care!