Did drain the transmission fluid from my 2007 Volvo XC90 3.2L though was surprised that only about 2 quarts came out. The capacity is listed as 7.4 quarts. While the car has a transmission cooler, would the other 5 quarts or so be there? How can I drain the approximately 5 additional quarts?

Here is a text description of changing the transmission fluid in short summary format. Some part names may not be exact.
The process to drain the transmission fluid was not that cumbersome, though harder than on other cars. Remove the plastic splash guard from underneath the car, then the transmission two part bolt is there. Place an 8 quart container under the bolt to catch the fluid, and first remove the small middle bolt with a T40 torx. Then remove the main transmission bolt with a 17mm allen hex key socket. After draining, replace the two part bolts. To fill, remove the air filter ECU from the air filter housing by unscrewing torx bolts and move it aside near the engine cover. Then remove the air filter housing with air filter which may require removing some air intake tubes. The transmission fill bolt should be visible then. Remove the bolt with a T55 torx and 1/2" breaker bar. It was tough to get it open. Then fill the fluid, and tighten the bolt to perhaps 26 ft-lb or other listed torque. Replace the air intake tubes and air filter housing with air filter and air filter ECU. Start the car, cycle through gears then warm up transmission fluid to specified temperature, turn off the car and drain the overflow fluid from the small T40 torx bolt. Replace the bolt. Replace the plastic splash cover.

XC90 Transmission Fill Bolt T55 torx

 

you don't drain the transmission fully to replace the fluid. There's two methods for freshing the fluid. You can do a "flush" which entails opening the oil cooler lines to let the transmission pump out the old fluid (into a bucket) and to suck in the fresh. you'd use clear hoses and run it until the pumped out fluid is red and clean. Check youtube for some how to vids. The other way (which doesn't risk damaging cooler lines or creating leaks) is the "drain/fill". So you've done the first cycle. Drain 2 quarts, put the plug in, add back the exact amount you drained then run the car for a few minutes. Repeat about 4X (like when when you use up a case of 12 quarts) and you'll be about 90% fresh fluid which will be red and clean. Finish up by properly setting the fluid level after a 10-15 minute drive cycle (use the warm line on the dipstick). If you have the 6 speed Aisin you don't set the level with the dipstick, those trannys use a fill tube and the level is set when the tranmission temp sensor indicates 55C (meaning you need a scanner that can read the transmission temp sensor)