The current in a series circuit remains the same through each resistor, regardless of the number of resistors on the circuit. This is because there is only one path for electrons to flow through.
However, it would be possible to change the current if the voltage of the source or the number of resistors was changed.
Using Ohm's Law (V=IR) to prove this, voltage and current are directly proportional. This means that an increase of voltage would mean an increase in current by the same amount.
Current and resistance are inversely proportional. If the total resistance of a series circuit is increased, the current decreases by that amount.