As I understood it, a charge-pump increases the input voltage by stages Vout=Vin(N+1). In my example, the two stages of charge-pumps, I have Vout=3Vin. So in case of Vin=5.5V this leads to Vout=5.5*(3)=16.5V which is OK for driving the switch(if the gate voltage requires more than 10V).
However, when the input voltage hits 20V, the Vout=20*(2+1)=60V which is too high for gate voltage of 10V. So, my question is: how can the same charge-pumps circuit is used for all the varying input voltage? See figure below (Allegro A4926 MOSFET Driver)