In a parallel combination of bulbs what we need to know is that the voltage is constant at every bulb and the current will distribute among the bulbs according to there efficiency. If the bulbs have same efficiency equal current will distribute among the bulbs.
When we add another bulb to the parallel circuit what happens is voltage remain constant and some current will transferred to the new bulb. So comparing with the initial situation now the bulbs get lower current hence their brightness will decrease.
Since we have one cell to supply power its efficiency is constant. In a parallel circuit voltage is also constant.
P = VI
P = Efficiency
V = Voltage
I = Current
Since P and V are constant I is also constant.
So finally what happen is the total voltage and current will remain same while bulbs decrease their brightness.
In the reference resister is equivalent to a bulb.