Voltage fluctuations

92 f150 302 automatic. I have a newer alternator in my truck and have switched it out to try another, but my voltage fluctuates erratically every once in a while. Usually happens when I have a lot of stuff running, lights, a/c, wipers, radio. Sometimes the signal lights even make the voltage needle tick back and forth. I know its not just the gauge, the lights will dim severely also. I'm pretty sure its not the alternator. I thought maybe if I beefed up the grounding system. Basically ground the battery to the frame and then ground several other things to the frame with some 0 gauge wire I have. Would this fix the problem or should I be looking for something else? This problem has actually ruined two 3 year warranty batteries.