All possible BJT circuits relating to polarity
The terms common-emitter, common-base, common-collector usually refer to transistors operating in a linear circuit, where output signal is proportional to input signal. Saturation or cut-off or reverse-bias modes would not be considered, only active (linear amplifying) mode.
However, some circuits do traverse between modes in operation - an oscillator starts off as a linear, and signals grow until a signal peak reaches a current cut-off or voltage saturation. In this case, a designer very likely adjusts circuit biasing to ensure one limit is reached before another so that resonator Q is not adversely degraded. We might refer to a "common-base oscillator" only because its small-signal operation mimics a common-base amplifier.

A SPICE model of a transistor accommodates all biasing polarity possibilities, and has no knowledge of common-base, common-emitter, common-collector.