Original Car Stereo Question?

The Devil invites you using a "Powered Subwoofer".

I would NOT recommend using powered subwoofers. The plate amplifier is mounted inside onto the enclosure and the subwoofer starts doing damage to the plate amplifier overtime. This also depends on how powerful the plate amplifier is. If the plate amplifier is over 300 watts, the subwoofer will destroy it up more faster.

Here's a photo of a plate amplifier. It's mounted inside onto the enclosure just like that with NO protection cap.

To answer your question, all you need to do is invest into aftermarket speakers.

That stereo is capable of sounding good with upgraded speakers. The front speakers are quite small (4 inch) and you'd be hard pressed to find a set that gives much bass, and where they mount is very tight. It would be better to put the front speakers in the door panels. The rear speakers are 5 1/4" so you might want to adopt something larger onto the rear deck. If you can squeeze a pair of 6x9s back there, there are good ones on the market. The tiny passenger compartment might lend itself  to a powered 8" subwoofer of a few hundred watts. 

In 1986, Toyota offered a special Fujitsu stereo that included AM stereo as well as normal FM stereo. If you have one of those, they are rare. Where I live in the San Francisco Bay Area there was one stereo AM broadcasting station- I heard it in the mid 1990's. It wasn't as dynamic as FM stereo, of course. It was a real special set giving 22 watts per channel- not earth shaking by any means, but with the windows closed it could drown out fire engine sirens.

If you want to have better sound, you will need to ditch BOTH head unit and speakers.  If you do not want to replace the old head unit, you can have a line output converter and an amp installed.  Get a subwoofer with its own amp too if you have some cash.  See a car audio shop.