How to get an output voltage of 16 Vpk on my preamplifier
You are looking for a overall voltage gain of about 40, which is certainly doable with two transistor stages.  That's a gain of about 6.5 per stage.  Fidelity and gain predictability is another matter, which your circuit is not well designed for.

The biggest loss of gain in your circuit is that you are loading the output with only 8 &Omega;.  That is guaranteed to heavily load the signal considering it is in part driven from a 500 &Omega; pullup.

You say this is a preamp, but the output impedances of each stage and particularly the final load impedance don't make sense for that.  You have rather low collector resistors of 500 &Omega;, which will limit the gain.  You have to decide what output impedance you really need from each stage.  What does this preamp need to drive?