As Tim hinted, maybe it's better thinking about gain and feedback.
Anyway, as a quick exercise I tried building such an amplifier. Using resistors, to get such swing you need very small resistances, a huge current in the order of 120mA, and the input impedance of the amplifier will be so low that you will have to drive it with a big buffer.
So a current source at the collector is the way to go. In that case, the only AC load will be 2800 Ohm, which with a swing of 4V peak will draw a max of about 4/2800 = 1.4 mA. If you don't want your transistor to saturate when the collector is at 2V from ground, Vce should be about 1V, and that means that the emitter resistor souldn't take more than about 1.2V or so. A good value seems to be a 100 Ohms, since at a quiescent current of 10mA it will take 1V, and at max sink it will take 1V + 1.4*100 = 1.14V, avoiding saturation. So I finally came up with the circuit attached below: the CE amplifier and the current source are complementary, to bias the circuit at 6V. The voltage gain is about 28, and the circuit can swing the full 8V, tough with quite a bit of distortion. I consider this a spice trick, since I had to tweak the emitter resistor of the pnp to get to the correct bias, and a small error causes a big change in the bias point: at this time in the morning I don't come up with a clean way to stabilize it
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