2 Channel System

Sorry to sound really remedial, but when setting up a 2 channel system, does it lack the highest highs and lowest lows? That is to say when setting up a dedicated 2 channel system - do you not hear all parts of musical passages - I am coming from a fairly solid car audio background where if you have a 3 or 4 way speaker system, you should get a separate tweeter and sub to get the full range...

So, would I have to round out my speaker system with any other "supplemental" speakers to hear all of the music?

A little help, please...

A "typical" speaker for a two channel system (you need 2, one for each channel) has either a tweeter and a woofer or a tweeter and a midrange and a woofer. Some folks add a subwoofer, some do not. Some also prefer a single "full range" driver for each channel, that does not have a separate woofer and tweeter.
And some use 3-way and 4-way speaker systems for stereo. The number of speakers has little to do with the frequency range.

I think you will find that most decent home 2 channel systems will outperform any car stereo in terms of overall quality. Many of the seperate drivers developed for car stereo applications have come about as a result of trying to overcome the many shortcomings of the auto listening environment, most of which are aimed at increasing the HF response. It has most always been rather simple to get mid and LF response in a car. I won't even mention the total lack of imaging in car audio. This is not meant as a slam, just an observation of two completely different applications.
I'm not a car guy, but I agree that 2 channel in the house is a very different animal. I'm probably like you though, because I build my speakers for two channel and "play" with crossovers and whatnot. In my opinion, you can get what you have in the car, in the house.....except for the sound pressure you can get in a car. For me, the minimum speaker needs to be a 2-way, but I prefer 3-way. After that it is the size of the system, just like the car. When I started out I liked huge watts and subwoofers in the house. Now I like the tight, fast bass I get from a really good 7" Scanspeak woofer and the nice mids and highs tube amps are capable of. One thing is for sure, when you get it right, two channel is very satisfying.