Cascaded common emitter amplifier
You can't.

A swing of 20mV seems like a pretty small signal -- but it's not small enough to have a reasonably linear current through a typical silicon diode.  So the emitter current of one of those transistor stages will be severely distorted with that large of a signal.

You need feedback to linearize the circuit.  Emitter degeneration would be easiest, but you may be able to do it using your existing shunt feedback and putting a resistor in series with each DC coupling capacitor.