Simply run speaker wire directly from the outputs on the amp to the speakers. It doesn't really matter which of the two wires you connect to each of the spades on the speaker, but however you do it you want them to be all wired uniformly.
If you're asking if you can run the same channels that are already running to your amp to additional speakers.. you will have to check the resistance of the speakers and the resistance that the amp is capable of running. For example, if your sub is 4ohm, and the speaker you're running on the same channel is 4ohm, then together they're 2ohm. If your amp isn't capable of doing 2ohm resistance then it will either throw the amp into protection mode (which it's unlikely that it will work afterwards).. or it will just fry the amp. Now if you're adding in tweeters you have a little more wiggle room as far as resistance, since the ohm load on the tweeters doesn't work quite like other speakers. Also, the crossover for tweeters should keep the ohms the same across the board.
Maybe I read that wrong and you're planning on installing a second amp, using the existing power wire? That should be fine as long as you pay attention to the amps (A) each amp draws and that the gauge of the wire is sufficient for the amp draw and length of the wire. You can find charts online that will show what gauge you need for how much amp draw with the length of wire you're running. I would just go by the fuse that's in each amp to estimate how much draw it has.. it will be overkill, but you'll know for sure that your wire is large enough. I suppose you could potentially end up with a ground loop interference using the same power wire, but it's not likely.. and if it does happen you will just need to run another wire.
I would definitely run separate grounds for each amp though. As short as possible, bolted into the chassis sanded bare.
A four channel amp will be better, and it will make a noticeable difference.. but good amps aren't cheap ($600-$1200+), and a four channel will be a good deal more expensive than a two channel amp of the same quality. Since the front speakers are far more important sound wise, if it comes down to a good two channel amp or a crummy four channel amp, I would get the two channel amp.