Yes, you can. If you are going to do this, I recommend getting a car stereo with preamp outputs, which you hook up to your home receiver/amplifier. You will need a 12v power supply, which you can buy at an electronics supply store. You should adjust the volume control on the car stereo to match the volume of other sources in your system.
If my memory is correct, you were asking about this in connection with why your home receiver did not receive stations as well as your car stereo. If you are going to buy the above for your home system for this purpose, I really think you should consider buying a vintage receiver or tuner to solve your reception problems, as it would probably be less expensive, and probably look better in your system. Of course, which will work better will depend on which specific models we are talking about.
You might also wish to take a look at:
http://fmtunerinfo.com/
I do not endorse everything they say (which I should not have to state, but, just in case...).