BJT Amplifier has different gain for negative and positive inputs
Your first two transistors look incorrectly biassed so that Ve is about (0.5*Vcc - 0.7V) in Q0, Q1 maybe slightly better.

This means (thanks to symmetry between Re and Rc (e.g.R0 and R3) that Vc is about Vcc/2+0.7V, in other words Vce=1.4V approx, and the transistor is close to saturation. 

First step : run a DC analysis to confirm this for both common-emitter stages (the emitter follower is fine).

To maximise the linear dynamic range you want to maximise the possible collector swing, so as a first pass, re-bias for Vc=9V, Ve=3V, i.e. Vb = 3.7V, calculate the base resistors for that - and see if it's improved.

This gives you up to 6V p-p swing at the collectors. It's not the best you can do as you have less AC swing at the emitter therefore you can increase headroom further, but I'll stop here.