Not sure what you mean be 'amplification voltage', but in this circuit, if the input V exceeds the supply, nothing more serious than distortion will occur.
If the input is extremely large, you would have to worry about power dissipation in the resistors and damage to the input NPN (above 6 V input because of VBE breakdown).
The circuit won't be able to generate an output higher than the supply.
A small signal model is applicable when the changes caused by the signal don't significantly affect the operating characteristics of the components (transistors). In the limit, this is an arbitrary small signal; anything else will cause distortion in the circuit.
For hand calculations, you might consider that signal swings more than 10 % of the bias current will cause detectable distortion; swings of 50 % of the bias current will cause easily observable (e.g. on an oscilloscope or simulation waveform) distortion of sinusoids or other waveforms.
Distortion can be mitigated by negative feedback -- your amplifier doesn't have any overall feedback. This amplifier has an extremely (unnecessarily ?) large amount of gain at AC (because of the bypass capacitors across the emitter resistors). Without any overall feedback, this amplifier will have distortion and clipping even with inputs of 1 mV. It could be complex to use negative feedback with this amplifier because of the large number of internal stages (and their associated poles and zeros).
The gain of each stage is approximately the collector load resistance divided by (26_mV/emitter_current); so the 1st stage gain is about 17).